Full Code of lettucecfd/lettuce for AI

Repository: lettucecfd/lettuce
Branch: master
Commit: 121359d2b7ee
Files: 256
Total size: 3.9 MB

Directory structure:
gitextract_tttiteof/

├── .codeclimate.yml
├── .github/
│   ├── ISSUE_TEMPLATE/
│   │   ├── BUG_REPORT.yml
│   │   └── FEATURE_REQUEST.yml
│   ├── pull_request_template.md
│   └── workflows/
│       └── CI.yml
├── .gitignore
├── .readthedocs.yaml
├── AUTHORS.rst
├── LICENSE
├── README.rst
├── docs/
│   ├── README.md
│   ├── authors.rst
│   ├── conf.py
│   ├── contributing.rst
│   ├── history.rst
│   ├── index.rst
│   ├── installation.rst
│   ├── make.bat
│   ├── modules.rst
│   ├── readme.rst
│   └── usage.rst
├── examples/
│   ├── 00_simplest_TGV.py
│   ├── 01a_first_example_TGV.ipynb
│   ├── 01b_first_example_obstacle.py
│   ├── 02_converging_obstacle_flow.py
│   ├── 03_outputs_TGV.py
│   ├── __init__.py
│   ├── advanced_flows/
│   │   ├── FailingTGVandObstacle.py
│   │   ├── LidDrivenCavity.ipynb
│   │   ├── MixingLayer.ipynb
│   │   ├── PartiallySaturatedObstacle.py
│   │   └── PorousMedium.ipynb
│   ├── advanced_projects/
│   │   ├── __init__.py
│   │   └── efficient_bounce_back_obstacle/
│   │       ├── 00_run_parametrized_project.ipynb
│   │       ├── 01_script_cylinder_simulation.py
│   │       ├── __init__.py
│   │       ├── auxiliary_code/
│   │       │   ├── __init__.py
│   │       │   ├── data_processing_and_plotting.py
│   │       │   └── helperCode.py
│   │       ├── boundary/
│   │       │   ├── __init__.py
│   │       │   ├── fullway_bounce_back_boundary.py
│   │       │   ├── halfway_bounce_back_boundary.py
│   │       │   ├── linear_interpolated_bounce_back_boundary.py
│   │       │   └── solid_boundary_data.py
│   │       ├── flow/
│   │       │   ├── __init__.py
│   │       │   └── obstacle_cylinder.py
│   │       ├── profile_reference_data/
│   │       │   ├── Fig09_ux_profile_pos1_DI2018.csv
│   │       │   ├── Fig09_ux_profile_pos1_KM2000.csv
│   │       │   ├── Fig09_ux_profile_pos1_LS1993.csv
│   │       │   ├── Fig09_ux_profile_pos1_WR2008.csv
│   │       │   ├── Fig09_ux_profile_pos2_DI2018.csv
│   │       │   ├── Fig09_ux_profile_pos2_KM2000.csv
│   │       │   ├── Fig09_ux_profile_pos2_LS1993.csv
│   │       │   ├── Fig09_ux_profile_pos2_WR2008.csv
│   │       │   ├── Fig09_ux_profile_pos3_DI2018.csv
│   │       │   ├── Fig09_ux_profile_pos3_KM2000.csv
│   │       │   ├── Fig09_ux_profile_pos3_LS1993.csv
│   │       │   ├── Fig09_ux_profile_pos3_WR2008.csv
│   │       │   ├── Fig10_uy_profile_pos1_DI2018.csv
│   │       │   ├── Fig10_uy_profile_pos1_KM2000.csv
│   │       │   ├── Fig10_uy_profile_pos1_LS1993.csv
│   │       │   ├── Fig10_uy_profile_pos1_WR2008.csv
│   │       │   ├── Fig10_uy_profile_pos2_DI2018.csv
│   │       │   ├── Fig10_uy_profile_pos2_KM2000.csv
│   │       │   ├── Fig10_uy_profile_pos2_LS1993.csv
│   │       │   ├── Fig10_uy_profile_pos2_WR2008.csv
│   │       │   ├── Fig10_uy_profile_pos3_DI2018.csv
│   │       │   ├── Fig10_uy_profile_pos3_KM2000.csv
│   │       │   ├── Fig10_uy_profile_pos3_LS1993.csv
│   │       │   ├── Fig10_uy_profile_pos3_WR2008.csv
│   │       │   ├── Fig11_uxux_profile_pos1_DI2018.csv
│   │       │   ├── Fig11_uxux_profile_pos1_KM2000.csv
│   │       │   ├── Fig11_uxux_profile_pos1_R2016.csv
│   │       │   ├── Fig11_uxux_profile_pos2_BM1994.csv
│   │       │   ├── Fig11_uxux_profile_pos2_DI2018.csv
│   │       │   ├── Fig11_uxux_profile_pos2_KM2000.csv
│   │       │   ├── Fig11_uxux_profile_pos2_LS1993.csv
│   │       │   ├── Fig11_uxux_profile_pos2_R2016.csv
│   │       │   ├── Fig11_uxux_profile_pos3_DI2018.csv
│   │       │   ├── Fig11_uxux_profile_pos3_KM2000.csv
│   │       │   ├── Fig11_uxux_profile_pos3_R2016.csv
│   │       │   ├── Fig12_uyuy_profile_pos1_DI2018.csv
│   │       │   ├── Fig12_uyuy_profile_pos1_R2016.csv
│   │       │   ├── Fig12_uyuy_profile_pos2_BM1994.csv
│   │       │   ├── Fig12_uyuy_profile_pos2_DI2018.csv
│   │       │   ├── Fig12_uyuy_profile_pos2_LS1993.csv
│   │       │   ├── Fig12_uyuy_profile_pos2_R2016.csv
│   │       │   ├── Fig12_uyuy_profile_pos3_DI2018.csv
│   │       │   ├── Fig12_uyuy_profile_pos3_R2016.csv
│   │       │   ├── Fig13_uxuy_profile_pos1_BM1994.csv
│   │       │   ├── Fig13_uxuy_profile_pos1_DI2018.csv
│   │       │   ├── Fig13_uxuy_profile_pos1_R2016.csv
│   │       │   ├── Fig13_uxuy_profile_pos2_BM1994.csv
│   │       │   ├── Fig13_uxuy_profile_pos2_DI2018.csv
│   │       │   ├── Fig13_uxuy_profile_pos2_LS1993.csv
│   │       │   ├── Fig13_uxuy_profile_pos2_R2016.csv
│   │       │   ├── Fig13_uxuy_profile_pos3_BM1994.csv
│   │       │   ├── Fig13_uxuy_profile_pos3_DI2018.csv
│   │       │   └── Fig13_uxuy_profile_pos3_R2016.csv
│   │       ├── reporter/
│   │       │   ├── __init__.py
│   │       │   ├── observables_force_coefficients.py
│   │       │   ├── reporter_ProfileReporter.py
│   │       │   └── reporter_advanced_vtk_reporter.py
│   │       └── simulation/
│   │           ├── __init__.py
│   │           └── ebb_simulation.py
│   ├── development/
│   │   ├── .gitignore
│   │   ├── example_progress_reporter_based_on_simplest_TGV.py
│   │   └── manually_generate_cuda_native.py
│   └── simple_flows/
│       ├── Couette.ipynb
│       ├── DecayingTurbulence.ipynb
│       ├── LambOseenVortex.py
│       ├── Obstacle.ipynb
│       └── Poiseuille.ipynb
├── lettuce/
│   ├── __init__.py
│   ├── _context.py
│   ├── _flow.py
│   ├── _simulation.py
│   ├── _stencil.py
│   ├── _unit.py
│   ├── _version.py
│   ├── base.py
│   ├── cli.py
│   ├── cuda_native/
│   │   ├── __init__.py
│   │   ├── _default_code_gen.py
│   │   ├── _generator.py
│   │   ├── _registry.py
│   │   ├── _template.py
│   │   ├── _transformer.py
│   │   ├── _util.py
│   │   └── ext/
│   │       ├── __init__.py
│   │       ├── _boundary/
│   │       │   ├── __init__.py
│   │       │   ├── bounce_back_boundary.py
│   │       │   ├── equilibrium_pu.py
│   │       │   └── no_boundary.py
│   │       ├── _collision/
│   │       │   ├── __init__.py
│   │       │   ├── bgk_collision.py
│   │       │   └── no_collision.py
│   │       ├── _equilibrium/
│   │       │   ├── __init__.py
│   │       │   └── quadratic_equilibrium.py
│   │       └── _force/
│   │           ├── __init__.py
│   │           └── _force.py
│   ├── ext/
│   │   ├── __init__.py
│   │   ├── _boundary/
│   │   │   ├── __init__.py
│   │   │   ├── anti_bounce_back_outlet.py
│   │   │   ├── bounce_back_boundary.py
│   │   │   ├── equilibrium_boundary_pu.py
│   │   │   ├── equilibrium_outlet_p.py
│   │   │   └── partially_saturated_boundary.py
│   │   ├── _collision/
│   │   │   ├── __init__.py
│   │   │   ├── bgk_collision.py
│   │   │   ├── kbc_collision.py
│   │   │   ├── mrt_collision.py
│   │   │   ├── no_collision.py
│   │   │   ├── regularized_collision.py
│   │   │   ├── smagorinsky_collision.py
│   │   │   └── trt_collision.py
│   │   ├── _equilibrium/
│   │   │   ├── __init__.py
│   │   │   ├── incompressible_quadratic_equilibrium.py
│   │   │   ├── quadratic_equilibrium.py
│   │   │   └── quadratic_equilibrium_less_memory.py
│   │   ├── _flows/
│   │   │   ├── __init__.py
│   │   │   ├── _ext_flow.py
│   │   │   ├── _flow_by_name.py
│   │   │   ├── couette.py
│   │   │   ├── decayingturbulence.py
│   │   │   ├── doublyshear.py
│   │   │   ├── lamboseenvortex.py
│   │   │   ├── liddrivencavity.py
│   │   │   ├── obstacle.py
│   │   │   ├── poiseuille.py
│   │   │   └── taylorgreen.py
│   │   ├── _force/
│   │   │   ├── __init__.py
│   │   │   ├── _force.py
│   │   │   ├── guo.py
│   │   │   └── shan_chen.py
│   │   ├── _reporter/
│   │   │   ├── __init__.py
│   │   │   ├── error_reporter.py
│   │   │   ├── failure_reporter.py
│   │   │   ├── observable_reporter.py
│   │   │   ├── progress_reporter.py
│   │   │   ├── vtk_reporter.py
│   │   │   └── write_image.py
│   │   └── _stencil/
│   │       ├── __init__.py
│   │       ├── d1q3.py
│   │       ├── d2q9.py
│   │       ├── d3q15.py
│   │       ├── d3q19.py
│   │       └── d3q27.py
│   └── util/
│       ├── __init__.py
│       ├── datautils.py
│       ├── moments.py
│       └── utility.py
├── native_cuda_synopsis.md
├── pyproject.toml
├── requirements.txt
├── tests/
│   ├── __init__.py
│   ├── boundary/
│   │   ├── test_antibounceback_outlet_bc.py
│   │   ├── test_bc_masks.py
│   │   ├── test_bounceback_bc.py
│   │   ├── test_equilibrium_bc_outlet_p.py
│   │   ├── test_equilibrium_bc_pu.py
│   │   ├── test_equilibrium_pressure_outlet.py
│   │   └── test_partiallysaturated_bc.py
│   ├── collision/
│   │   ├── test_collision_conserves_mass.py
│   │   ├── test_collision_conserves_momentum.py
│   │   ├── test_collision_fixpoint_2x.py
│   │   ├── test_collision_fixpoint_2x_MRT.py
│   │   ├── test_collision_optimizes_pseudo_entropy.py
│   │   ├── test_collision_relaxes_shear_moments.py
│   │   └── test_force.py
│   ├── conftest.py
│   ├── flow/
│   │   ├── test_divergence.py
│   │   ├── test_einsum.py
│   │   ├── test_flow.py
│   │   ├── test_initialize_fneq.py
│   │   ├── test_initialize_pressure.py
│   │   ├── test_obstacle.py
│   │   └── test_pressure_poisson.py
│   ├── moments/
│   │   ├── test_conserved_moments_d2q9.py
│   │   ├── test_getitem.py
│   │   ├── test_inverse_transform.py
│   │   ├── test_moment_equilibrium_D3Q27Hermite.py
│   │   ├── test_moment_equilibrium_dellar.py
│   │   ├── test_moment_equilibrium_lallemand.py
│   │   ├── test_moments_density.py
│   │   └── test_orthogonality.py
│   ├── native/
│   │   ├── __init__.py
│   │   ├── test_native_bgk_collision.py
│   │   ├── test_native_bounce_back.py
│   │   ├── test_native_equilibrium_pu.py
│   │   ├── test_native_no_streaming_mask.py
│   │   ├── test_native_streaming.py
│   │   └── test_native_streaming_strategy.py
│   ├── reporter/
│   │   ├── test_HDF5Reporter.py
│   │   ├── test_energy_spectrum.py
│   │   ├── test_generic_reporters.py
│   │   ├── test_high_ma_reporter.py
│   │   ├── test_nan_reporter.py
│   │   ├── test_vtk_reporter_mask.py
│   │   ├── test_vtk_reporter_no_mask.py
│   │   ├── test_write_image.py
│   │   └── test_write_vtk.py
│   ├── stencil/
│   │   ├── test_first_zero.py
│   │   ├── test_opposite.py
│   │   ├── test_symmetry.py
│   │   └── test_weights.py
│   ├── test_checkpoint.py
│   ├── test_cli.py
│   ├── test_equilibrium.py
│   ├── unit/
│   │   ├── __init__.py
│   │   ├── test_consistency.py
│   │   ├── test_conversion_reversible.py
│   │   └── test_reynolds_number_consistent.py
│   └── util/
│       ├── test_grid_fine_to_coarse.py
│       └── test_torch_gradient.py
└── versioneer.py

================================================
FILE CONTENTS
================================================

================================================
FILE: .codeclimate.yml
================================================
exclude_patterns:
    - "versioneer.py"
    - "lettuce/_version.py"
    - "config/"
    - "db/"
    - "dist/"
    - "features/"
    - "**/node_modules/"
    - "script/"
    - "**/spec/"
    - "**/test/"
    - "**/tests/"
    - "Tests/"
    - "**/vendor/"
    - "**/*_test.go"
    - "**/*.d.ts"


================================================
FILE: .github/ISSUE_TEMPLATE/BUG_REPORT.yml
================================================
name: Bug Report
description: File a bug report.
title: "[Bug]: "
labels: ["bug"]
assignees: []
body:
  - type: markdown
    attributes:
      value: |
        Thanks for taking the time to fill out this bug report!
  - type: input
    id: contact
    attributes:
      label: Contact Details
      description: How can we get in touch with you if we need more info?
      placeholder: ex. email@example.com
    validations:
      required: false
  - type: textarea
    id: what-happened
    attributes:
      label: What happened?
      description: Also tell us, what did you expect to happen?
      placeholder: Tell us what you see!
      value: "A bug happened!"
    validations:
      required: true
  - type: dropdown
    id: version
    attributes:
      label: Version
      description: What version of our software are you running?
      options:
        - 0.2.0
        - 0.2.1
        - 0.2.2
        - 0.2.3
      default: 0
    validations:
      required: true
  - type: dropdown
    id: browsers
    attributes:
      label: What operating system are you seeing the problem on?
      multiple: true
      options:
        - Linux
        - Windows
        - MacOs
  - type: textarea
    id: logs
    attributes:
      label: Relevant log output
      description: Please copy and paste any relevant log output. This will be automatically formatted into code, so no need for backticks.
      render: shell


================================================
FILE: .github/ISSUE_TEMPLATE/FEATURE_REQUEST.yml
================================================
name: "Feature Request"
description: Suggest an idea for improving lettuce
title: "[Feature]: "
labels: ["enhancement"]
assignees: []
body:
  - type: markdown
    attributes:
      value: |
        Thanks for suggesting a new and exciting feature!
  - type: input
    id: contact
    attributes:
      label: Contact Details
      description: How can we get in touch with you if we need more info?
      placeholder: ex. email@example.com
    validations:
      required: false
  - type: textarea
    id: is-related
    attributes:
      label: Is your proposal related to a problem?
      description: Provide a clear and concise description of what the problem is.
      placeholder: "I'm always frustrated when..."
      value: "This is related to a problem!"
    validations:
      required: true
  - type: textarea
    id: solution
    attributes:
      label: "Describe the solution you'd like"
      description: Provide a clear and concise description of what you want to happen.
      placeholder: (Describe your proposed solution here.)
      value: "This is the suggested solution."
    validations:
      required: true
  - type: textarea
    id: alternatives
    attributes:
      label: "Describe alternatives you've considered"
      description: "Let us know about other solutions you've tried or researched."
      placeholder: (Write your answer here.)
      value: "This is an alternative."
    validations:
      required: true
  - type: textarea
    id: context
    attributes:
      label: "Additional context"
      description: "Is there anything else you can add about the proposal? You might want to link to related issues here, if you haven't already."
      placeholder: (Write your answer here.)
      value: "This is additional context."
    validations:
      required: true
      


================================================
FILE: .github/pull_request_template.md
================================================
## Description

<!-- Add a description of the changes -->

## Checklist

 - [ ] This pull request is associated to an issue
 - [ ] This PR contains a description
 - [ ] Did you add a new method? If so, you need to
   - [ ] add method description
   - [ ] maybe mention class in the corresponding `__init__`
   - [ ] add an example using the method in `examples/advanced_flows/` or `examples/simple_flows/`
   - [ ] add a test in `tests/`
 - [ ] Add someone else as reviewer and wait for approval before merging.


================================================
FILE: .github/workflows/CI.yml
================================================
name: CI

on:
  push:
    branches:
      - "master"
  pull_request:
    branches:
      - "**"
  schedule:

    - cron: "0 7 * * 1"

  # Allows you to run this workflow manually from the Actions tab
  workflow_dispatch:

jobs:
  test:
    runs-on: ${{ matrix.cfg.os }}
    strategy:
      fail-fast: false
      matrix:
        cfg:
          - { os: ubuntu-latest, python-version: '3.12', extra: 'cpu' }
          - { os: ubuntu-latest, python-version: '3.12', extra: 'cu124' }
          - { os: ubuntu-latest, python-version: '3.12', extra: 'cu126' }
          - { os: ubuntu-latest, python-version: '3.12', extra: 'cu128' }
          - { os: ubuntu-latest, python-version: '3.12', extra: 'cu130' }
          - { os: macos-latest, python-version: '3.12', extra: 'cpu' }

    steps:
      - uses: actions/checkout@v4

      - name: Install uv
        uses: astral-sh/setup-uv@v6

      - name: Install dependencies with ${{ matrix.cfg.extra }} extra
        shell: bash -el {0}
        run: |
          uv sync --extra ${{ matrix.cfg.extra }}

      - name: Run unit tests
        shell: bash -el {0}
        run: |
          uv run --extra ${{ matrix.cfg.extra }} pytest tests

      - name: Run integration tests
        shell: bash -el {0}
        run: |
          source .venv/bin/activate
          if [[ "${{ matrix.cfg.extra }}" == "cpu" ]]; then
            lettuce --no-cuda convergence --use-no-cuda_native
            lettuce --no-cuda benchmark --use-no-cuda_native
          else
            lettuce --no-cuda convergence --use-no-cuda_native
            lettuce --no-cuda benchmark --use-no-cuda_native
          fi


================================================
FILE: .gitignore
================================================
Makefile
.idea/
.gitattributes
.editorconfig

# Byte-compiled / optimized / DLL files
__pycache__/
*.py[cod]
*$py.class

# C extensions
*.so

# Distribution / packaging
.Python
env/
build/
develop-eggs/
dist/
downloads/
eggs/
.eggs/
lib/
lib64/
parts/
sdist/
var/
wheels/
*.egg-info/
.installed.cfg
*.egg

# PyInstaller
#  Usually these files are written by a python script from a template
#  before PyInstaller builds the exe, so as to inject date/other infos into it.
*.manifest
*.spec

# Installer logs
pip-log.txt
pip-delete-this-directory.txt

# Unit test / coverage reports
htmlcov/
.tox/
.coverage
.coverage.*
.cache
nosetests.xml
coverage.xml
*.cover
.hypothesis/
.pytest_cache/

# Translations
*.mo
*.pot

# Django stuff:
*.log
local_settings.py

# Flask stuff:
instance/
.webassets-cache

# Scrapy stuff:
.scrapy

# Sphinx documentation
docs/_build/

# PyBuilder
target/

# Jupyter Notebook
.ipynb_checkpoints

# pyenv
.python-version

# celery beat schedule file
celerybeat-schedule

# SageMath parsed files
*.sage.py

# dotenv
.env

# virtualenv
.venv
venv/
ENV/

# Spyder project settings
.spyderproject
.spyproject

# Rope project settings
.ropeproject

# mkdocs documentation
/site

# mypy
.mypy_cache/

# data folder
data/


================================================
FILE: .readthedocs.yaml
================================================
# .readthedocs.yaml
# Read the Docs configuration file
# See https://docs.readthedocs.io/en/stable/config-file/v2.html for details

# Required
version: 2

# Set the OS, Python version and other tools you might need
build:
  os: ubuntu-22.04
  tools:
    python: "3.12"
    # You can also specify other tool versions:
    # nodejs: "19"
    # rust: "1.64"
    # golang: "1.19"

# Build documentation in the "docs/" directory with Sphinx
sphinx:
  configuration: docs/conf.py

# Optionally build your docs in additional formats such as PDF and ePub
# formats:
#    - pdf
#    - epub

# Optional but recommended, declare the Python requirements required
# to build your documentation
# See https://docs.readthedocs.io/en/stable/guides/reproducible-builds.html
python:
   install:
   - requirements: requirements.txt


================================================
FILE: AUTHORS.rst
================================================
=======
Credits
=======

Development Lead
----------------

* Andreas Kraemer <kraemer.research@gmail.com>

Contributors
------------

* Dominik Wilde
* Mario Bedrunka
* Philipp Spelten
* You?


================================================
FILE: LICENSE
================================================
MIT License

Copyright (c) 2019, Andreas Kraemer

Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.



================================================
FILE: README.rst
================================================
.. image:: https://raw.githubusercontent.com/lettucecfd/lettuce/master/.source/img/logo_lettuce_typo.png

.. image:: https://github.com/lettucecfd/lettuce/actions/workflows/CI.yml/badge.svg
        :target: https://github.com/lettucecfd/lettuce/actions/workflows/CI.yml
        :alt: CI Status

.. image:: https://readthedocs.org/projects/lettucecfd/badge/?version=latest
        :target: https://lettucecfd.readthedocs.io/en/latest/?badge=latest
        :alt: Documentation Status
        
.. image:: https://zenodo.org/badge/DOI/10.5281/zenodo.3757641.svg
        :target: https://doi.org/10.5281/zenodo.3757641



GPU-accelerated Lattice Boltzmann Simulations in Python
-------------------------------------------------------

Lettuce is a Computational Fluid Dynamics framework based on the lattice Boltzmann method (LBM).

- **GPU-Accelerated Computation**: Utilizes PyTorch for high performance and efficient GPU utilization.
- **Rapid Prototyping**: Supports both 2D and 3D simulations for quick and reliable analysis.
- **Advanced Techniques**: Integrates neural networks and automatic differentiation to enhance LBM.
- **Optimized Performance**: Includes custom PyTorch extensions for native CUDA kernels.

Resources
---------

- `Documentation`_
- Presentation at CFDML2021 - `Paper`_ | `Preprint`_ | `Slides`_ | `Video`_ | `Code`_

.. _Paper: https://www.springerprofessional.de/en/lettuce-pytorch-based-lattice-boltzmann-framework/19862378
.. _Documentation: https://lettuceboltzmann.readthedocs.io
.. _Preprint: https://arxiv.org/pdf/2106.12929.pdf
.. _Slides: https://drive.google.com/file/d/1jyJFKgmRBTXhPvTfrwFs292S4MC3Fqh8/view
.. _Video: https://www.youtube.com/watch?v=7nVCuuZDCYA
.. _Code: https://github.com/lettucecfd/lettuce-paper

Getting Started
---------------

To find some very simple examples of how to use lettuce, please have a look at the examples_. These will guide you through lettuce's main features. Please ensure you have Jupyter installed to run the Jupyter notebooks.

.. _examples: https://github.com/lettucecfd/lettuce/tree/master/examples

Installation
------------

* Install the uv package manager from https://docs.astral.sh/uv/

* Clone this repository from github and change to it::

    git clone https://github.com/lettucecfd/lettuce
    cd lettuce

* Create a new virtual environment and activate it::

    uv venv
    source .venv/bin/activate

* The `pyproject.toml` file currently requires at least **CUDA 12.4** (we successfully tested CUDA 12.4, 12.6, 12.8 and 13.0). If your GPU does not support this version, you may need to downgrade it. Please note that we cannot guarantee the maintenance for older CUDA versions.

* Run the install command, depending on your needs (run one of the three options below):

        1. use lettuce (no development) with GPU support::

                uv pip install .

        2. use lettuce (no development) with CPU only or specific older CUDA versions (if you do not have access to a GPU or an older GPU) use (cpu, cu124, cu126)::

                uv pip install ".[cpu]"

        3. use and **develop** lettuce (code changes take effect in program execution): use the changeable-installation-flag (`-e`)::

                uv pip install -e .

* Check out the convergence order, running on CPU::

    lettuce --no-cuda convergence

* For running a CUDA-driven LBM simulation on one GPU omit the `--no-cuda`. If CUDA is not found, make sure that CUDA-capable GPU drivers are installed and compatible with the installed cudatoolkit (check cuda version number).

* Check out the performance, running on GPU::

    lettuce benchmark

* Run the test cases::

    pytest tests

Citation
--------
If you use Lettuce in your research, please cite the following paper::

    @inproceedings{bedrunka2021lettuce,
      title={Lettuce: PyTorch-Based Lattice Boltzmann Framework},
      author={Bedrunka, Mario Christopher and Wilde, Dominik and Kliemank, Martin and Reith, Dirk and Foysi, Holger and Kr{\"a}mer, Andreas},
      booktitle={High Performance Computing: ISC High Performance Digital 2021 International Workshops, Frankfurt am Main, Germany, June 24--July 2, 2021, Revised Selected Papers},
      pages={40},
      organization={Springer Nature}
    }

Credits
-------
We use the following third-party packages:

* pytorch_
* numpy_
* pytest_
* click_
* matplotlib_
* versioneer_
* pyevtk_
* h5py_
* mmh3_


This package was created with Cookiecutter_ and the `audreyr/cookiecutter-pypackage`_ project template.

.. _Cookiecutter: https://github.com/audreyr/cookiecutter
.. _`audreyr/cookiecutter-pypackage`: https://github.com/audreyr/cookiecutter-pypackage

.. _pytorch: https://github.com/pytorch/pytorch
.. _numpy: https://github.com/numpy/numpy
.. _pytest: https://github.com/pytest-dev/pytest
.. _click: https://github.com/pallets/click
.. _matplotlib: https://github.com/matplotlib/matplotlib
.. _versioneer: https://github.com/python-versioneer/python-versioneer
.. _pyevtk: https://github.com/pyscience-projects/pyevtk
.. _h5py: https://github.com/h5py/h5py
.. _mmh3: https://github.com/hajimes/mmh3

License
-----------
* Free software: MIT license, as found in the LICENSE_ file.

.. _LICENSE: https://github.com/lettucecfd/lettuce/blob/master/LICENSE



================================================
FILE: docs/README.md
================================================
# Building the docs locally

```
conda install -c conda-forge \
    sphinx \
    sphinxcontrib-napoleon \
    numpydoc \
    alabaster

cd docs
make html
```




================================================
FILE: docs/authors.rst
================================================
.. include:: ../AUTHORS.rst


================================================
FILE: docs/conf.py
================================================
#!/usr/bin/env python
# -*- coding: utf-8 -*-
#
# lettuce documentation build configuration file, created by
# sphinx-quickstart on Fri Jun  9 13:47:02 2017.
#
# This file is execfile()d with the current directory set to its
# containing dir.
#
# Note that not all possible configuration values are present in this
# autogenerated file.
#
# All configuration values have a default; values that are commented out
# serve to show the default.

# If extensions (or modules to document with autodoc) are in another
# directory, add these directories to sys.path here. If the directory is
# relative to the documentation root, use os.path.abspath to make it
# absolute, like shown here.
#
import os
import sys

sys.path.insert(0, os.path.abspath('..'))

import lettuce

# -- General configuration ---------------------------------------------

# If your documentation needs a minimal Sphinx version, state it here.
#
# needs_sphinx = '1.0'

# Add any Sphinx extension module names here, as strings. They can be
# extensions coming with Sphinx (named 'sphinx.ext.*') or your custom ones.
extensions = ['sphinx.ext.autodoc', 'sphinx.ext.viewcode', 'sphinx.ext.napoleon']

# Add any paths that contain templates here, relative to this directory.
templates_path = ['_templates']

# The suffix(es) of source filenames.
# You can specify multiple suffix as a list of string:
#
# source_suffix = ['.rst', '.md']
source_suffix = '.rst'

# The master toctree document.
master_doc = 'index'

# General information about the project.
project = u'lettuce'
copyright = u"2019, Andreas Kraemer"
author = u"Andreas Kraemer"

# The version info for the project you're documenting, acts as replacement
# for |version| and |release|, also used in various other places throughout
# the built documents.
#
# The short X.Y version.
version = lettuce.__version__
# The full version, including alpha/beta/rc tags.
release = lettuce.__version__

# The language for content autogenerated by Sphinx. Refer to documentation
# for a list of supported languages.
#
# This is also used if you do content translation via gettext catalogs.
# Usually you set "language" from the command line for these cases.
language = None

# List of patterns, relative to source directory, that match files and
# directories to ignore when looking for source files.
# This patterns also effect to html_static_path and html_extra_path
exclude_patterns = ['_build', 'Thumbs.db', '.DS_Store']

# The name of the Pygments (syntax highlighting) style to use.
pygments_style = 'sphinx'

# If true, `todo` and `todoList` produce output, else they produce nothing.
todo_include_todos = False

# -- Options for HTML output -------------------------------------------

# The theme to use for HTML and HTML Help pages.  See the documentation for
# a list of builtin themes.
#
html_theme = 'alabaster'

# Theme options are theme-specific and customize the look and feel of a
# theme further.  For a list of options available for each theme, see the
# documentation.
#
# html_theme_options = {}

# Add any paths that contain custom static files (such as style sheets) here,
# relative to this directory. They are copied after the builtin static files,
# so a file named "default.css" will overwrite the builtin "default.css".
html_static_path = ['_static']

# -- Options for HTMLHelp output ---------------------------------------

# Output file base name for HTML help builder.
htmlhelp_basename = 'lettucedoc'

# -- Options for LaTeX output ------------------------------------------

latex_elements = {
    # The paper size ('letterpaper' or 'a4paper').
    #
    # 'papersize': 'letterpaper',

    # The font size ('10pt', '11pt' or '12pt').
    #
    # 'pointsize': '10pt',

    # Additional stuff for the LaTeX preamble.
    #
    # 'preamble': '',

    # Latex figure (float) alignment
    #
    # 'figure_align': 'htbp',
}

# Grouping the document tree into LaTeX files. List of tuples
# (source start file, target name, title, author, documentclass
# [howto, manual, or own class]).
latex_documents = [
    (master_doc, 'lettuce.tex',
     u'lettuce Documentation',
     u'Andreas Kraemer', 'manual'),
]

# -- Options for manual page output ------------------------------------

# One entry per manual page. List of tuples
# (source start file, name, description, authors, manual section).
man_pages = [
    (master_doc, 'lettuce',
     u'lettuce Documentation',
     [author], 1)
]

# -- Options for Texinfo output ----------------------------------------

# Grouping the document tree into Texinfo files. List of tuples
# (source start file, target name, title, author,
#  dir menu entry, description, category)
texinfo_documents = [
    (master_doc, 'lettuce',
     u'lettuce Documentation',
     author,
     'lettuce',
     'One line description of project.',
     'Miscellaneous'),
]


================================================
FILE: docs/contributing.rst
================================================
.. include:: ../CONTRIBUTING.rst


================================================
FILE: docs/history.rst
================================================
.. include:: ../HISTORY.rst


================================================
FILE: docs/index.rst
================================================
Welcome to lettuce's documentation!
======================================

.. toctree::
   :maxdepth: 2
   :caption: Contents:

   readme
   installation
   usage
   modules
   contributing
   authors
   history

Indices and tables
==================
* :ref:`genindex`
* :ref:`modindex`
* :ref:`search`


================================================
FILE: docs/installation.rst
================================================
.. highlight:: shell

============
Installation
============


From sources
------------

The sources for lettuce can be downloaded from the `Github repo`_.

You can either clone the public repository:

.. code-block:: console

    $ git clone git://github.com/lettucecfd/lettuce

Or download the `tarball`_:

.. code-block:: console

    $ curl  -OL https://github.com/lettucecfd/lettuce/tarball/master

Once you have a copy of the source, you can install it with:

.. code-block:: console

    $ python setup.py install


.. _Github repo: https://github.com/lettucecfd/lettuce
.. _tarball: https://github.com/lettucecfd/lettuce/tarball/master


================================================
FILE: docs/make.bat
================================================
@ECHO OFF

pushd %~dp0

REM Command file for Sphinx documentation

if "%SPHINXBUILD%" == "" (
	set SPHINXBUILD=python -msphinx
)
set SOURCEDIR=.
set BUILDDIR=_build
set SPHINXPROJ=lettuce

if "%1" == "" goto help

%SPHINXBUILD% >NUL 2>NUL
if errorlevel 9009 (
	echo.
	echo.The Sphinx module was not found. Make sure you have Sphinx installed,
	echo.then set the SPHINXBUILD environment variable to point to the full
	echo.path of the 'sphinx-build' executable. Alternatively you may add the
	echo.Sphinx directory to PATH.
	echo.
	echo.If you don't have Sphinx installed, grab it from
	echo.http://sphinx-doc.org/
	exit /b 1
)

%SPHINXBUILD% -M %1 %SOURCEDIR% %BUILDDIR% %SPHINXOPTS%
goto end

:help
%SPHINXBUILD% -M help %SOURCEDIR% %BUILDDIR% %SPHINXOPTS%

:end
popd


================================================
FILE: docs/modules.rst
================================================
API
===

Simulation
----------
.. automodule:: lettuce.simulation
    :noindex:
    :members:
    :undoc-members:
    :show-inheritance:


Lattices
--------
.. automodule:: lettuce.lattices
    :noindex:
    :members:
    :undoc-members:
    :show-inheritance:


Stencils
--------
.. automodule:: lettuce.stencils
    :noindex:
    :members:
    :undoc-members:
    :show-inheritance:


Streaming
---------
.. automodule:: lettuce.streaming
    :noindex:
    :members:
    :undoc-members:
    :show-inheritance:


Collision
---------
.. automodule:: lettuce.collision
    :noindex:
    :members:
    :undoc-members:
    :show-inheritance:


Observables
-----------
.. automodule:: lettuce.observables
    :noindex:
    :members:
    :undoc-members:
    :show-inheritance:


Reporters
---------
.. automodule:: lettuce.reporters
    :noindex:
    :members:
    :undoc-members:
    :show-inheritance:


Force
-----
.. automodule:: lettuce.force
    :noindex:
    :members:
    :undoc-members:
    :show-inheritance:


Equilibrium
-----------
.. automodule:: lettuce.equilibrium
    :noindex:
    :members:
    :undoc-members:
    :show-inheritance:


Boundary
--------
.. automodule:: lettuce.boundary
    :noindex:
    :members:
    :undoc-members:
    :show-inheritance:


Flows
-----

Couette
^^^^^^^
.. automodule:: lettuce.flows.couette
    :noindex:
    :members:
    :undoc-members:
    :show-inheritance:

Poiseuille
^^^^^^^^^^
.. automodule:: lettuce.flows.poiseuille
    :noindex:
    :members:
    :undoc-members:
    :show-inheritance:

Taylor-Green
^^^^^^^^^^^^
.. automodule:: lettuce.flows.taylorgreen
    :noindex:
    :members:
    :undoc-members:
    :show-inheritance:

Decaying-Turbulence
^^^^^^^^^^^^^^^^^^^
.. automodule:: lettuce.flows.decayingturbulence
    :noindex:
    :members:
    :undoc-members:
    :show-inheritance:

Obstacle
^^^^^^^^
.. automodule:: lettuce.flows.obstacle
    :noindex:
    :members:
    :undoc-members:
    :show-inheritance:

Utility
-------
.. automodule:: lettuce.util
    :noindex:
    :members:
    :undoc-members:
    :show-inheritance:


Command-Line Interface
----------------------
.. automodule:: lettuce.cli
    :noindex:
    :members:
    :undoc-members:
    :show-inheritance:


================================================
FILE: docs/readme.rst
================================================
.. include:: ../README.rst


================================================
FILE: docs/usage.rst
================================================
=====
Usage
=====

To use lettuce in a project::

    import lettuce


================================================
FILE: examples/00_simplest_TGV.py
================================================
"""
This file showcases the simplicity of the lettuce code.
The following code will run a two-dimensional Taylor-Green vortex on GPU.
"""

import torch
import lettuce as lt

flow = lt.TaylorGreenVortex(
    lt.Context(dtype=torch.float64),  # for running on cpu: device='cpu'
    resolution=128,
    reynolds_number=100,
    mach_number=0.05,
    stencil=lt.D2Q9
)
simulation = lt.Simulation(
    flow=flow,
    collision=lt.BGKCollision(tau=flow.units.relaxation_parameter_lu),
    reporter=[])
mlups = simulation(num_steps=1000)
print("Performance in MLUPS:", mlups)


================================================
FILE: examples/01a_first_example_TGV.ipynb
================================================
{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# A first example\n",
    "This is a first example of how to use lettuce.\n",
    "A two dimensional Taylor Green vortex is initialized and simulated for 10000 steps. Afterwards the energy and the velocity field is plotted."
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-08-04T07:24:40.895024Z",
     "start_time": "2024-08-04T07:24:39.958634Z"
    }
   },
   "source": [
    "import lettuce as lt\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import torch"
   ],
   "outputs": [],
   "execution_count": 1
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Setup\n",
    "* for running on GPU: device = \"cuda\". CUDA drivers are required!\n",
    "* dtype=torch.float32 for single precision - float64 for double precision\n",
    "* select collision model (here BGKCollision) - try also KBCCollision or RegularizedCollision"
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-08-04T07:24:43.170453Z",
     "start_time": "2024-08-04T07:24:43.005785Z"
    }
   },
   "source": [
    "context = lt.Context(device=torch.device('cuda:0') if torch.cuda\n",
    "                     .is_available() else torch.device('cpu'),\n",
    "                     dtype=torch.float32)\n",
    "flow = lt.TaylorGreenVortex(resolution=256, reynolds_number=100, \n",
    "                            mach_number=0.05, stencil=lt.D2Q9,\n",
    "                            context=context)\n",
    "collision = lt.BGKCollision(tau=flow.units.relaxation_parameter_lu)\n",
    "energyreporter = lt.ObservableReporter(lt.IncompressibleKineticEnergy(flow), interval=1000, out=None)\n",
    "simulation = lt.Simulation(flow=flow, collision=collision, reporter=[energyreporter])"
   ],
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "steps     time     IncompressibleKineticEnergy\n"
     ]
    }
   ],
   "execution_count": 2
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Reporters will grab the results in between simulation steps (see reporters.py and simulation.py)\n",
    "* Output: Column 1: simulation steps, Column 2: time in LU, Column 3: kinetic energy in PU\n",
    "* Output: separate VTK-file with ux,uy,(uz) and p for every 100. time step in ./output"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Run simulation"
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-08-04T07:24:50.269735Z",
     "start_time": "2024-08-04T07:24:45.023922Z"
    }
   },
   "source": [
    "mlups = simulation(10000)\n",
    "print(\"Performance in MLUPS:\", mlups)"
   ],
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Performance in MLUPS: 124.98567838266325\n"
     ]
    }
   ],
   "execution_count": 3
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Post process\n",
    "### Energy Reporter\n",
    "* Grab output of kinetic energy reporter"
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-08-04T07:24:50.400266Z",
     "start_time": "2024-08-04T07:24:50.270799Z"
    }
   },
   "source": [
    "energy = np.array(simulation.reporter[0].out)\n",
    "print(energy.shape)\n",
    "plt.plot(energy[:,1],energy[:,2])\n",
    "plt.title('Kinetic energy')\n",
    "plt.xlabel('Time')\n",
    "plt.ylabel('Energy in physical units')\n",
    "plt.show()"
   ],
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(11, 3)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "execution_count": 4
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Velocity\n",
    "We calculate the speed in Lettuce units depending on the last 'f'. Then we convert this velocity into physical units. For further investigations the tensor must be converted into a Numpy-Array. The norm of the fractions in x and y direction is plotted afterwards."
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-08-04T07:25:00.256202Z",
     "start_time": "2024-08-04T07:25:00.174826Z"
    }
   },
   "source": [
    "u = flow.u_pu.cpu().numpy()\n",
    "u_norm = np.linalg.norm(u,axis=0)\n",
    "plt.imshow(u_norm)\n",
    "plt.show()"
   ],
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "execution_count": 6
  },
  {
   "metadata": {},
   "cell_type": "code",
   "outputs": [],
   "execution_count": null,
   "source": ""
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
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================================================
FILE: examples/01b_first_example_obstacle.py
================================================
import torch
import lettuce as lt
import matplotlib.pyplot as plt
import numpy as np

"""
Context definitions.

The context defines the default device (cpu or cuda) and datatype (e.g.,
float32 for single, float64 for double precision).
Native CUDA is currently not supported for the anti-bounce-back outlet.
"""
context = lt.Context(torch.device("cuda:0"), use_native=False)

"""
Flow definitions.

We need
1. the resolution in x and y direction
2. the Reynolds number (i.e., how fast the flow behaves compared to the
    object's length and fluid's viscosity)
3. the Mach number (i.e., how fast the flow is compared to speed of sound;
    Ma=0.3 is stable, above is discouraged)
4. the physical domain length in x-direction (this defines how lattice units
    scale to physical units)
to initialize the Obstacle flow object.
"""
nx = 200
ny = 100
Re = 300
Ma = 0.01
lx = 1

flow = lt.Obstacle(context, [nx, ny], reynolds_number=Re, mach_number=Ma,
                   domain_length_x=lx)

"""
Per default, lt.Obstacle has no solid. It is stored in flow.mask as a fully
False numpy array.
To add a solid, we set some mask values to True by getting the domain extends
from flow.grid and creating a boolean array from it.

For a circle, just use a boolean function. Otherwise, you may as well use the
array indices.
"""
x, y = flow.grid
r = .05*y.max()      # radius
x_c = 0.3*x.max()   # center along x
y_c = 0.5*y.max()   # center along y
flow.mask = ((x - x_c) ** 2 + (y - y_c) ** 2) < (r ** 2)

"""
To show 2D images, you need to rotate the outputs. This is because in lettuce,
the first axis is downstream, while for imshow it is vertical.
"""
plt.imshow(context.convert_to_ndarray(flow.mask.t()))
plt.show()

"""
Collision definition.

The collision is usually BGK (low dissipation, but may be unstable) or KBC
(higher dissipation, but generally stable). BGK is preferred for converging
flows, KBC is preferred for driven flows in smaller domains (where energy
conversation plays a smaller role, but gradients may be higher).
"""
collision = lt.KBCCollision(tau=flow.units.relaxation_parameter_lu)

"""
Simulation object setup.
"""
simulation = lt.Simulation(flow=flow, collision=collision, reporter=[])

"""
Reporters.

- Reporter objects are used to extract information later on or during the
    simulation.
- They can be created as separate objects when required later
    (see 01_example4convergence.py).
"""

energyreporter = lt.ObservableReporter(lt.IncompressibleKineticEnergy(flow),
                                       interval=50)
simulation.reporter.append(energyreporter)

"""
Run num_steps iterations of the simulation.
This can be done repeatedly (see 02_converging_flows.py).
"""
mlups = simulation(num_steps=4000)
print("Performance in MLUPS:", mlups)

"""
Before or after simulation call, physical values can be extracted from the
flow.
Alternatively, the reporters can be drawn from the simulation.reporters list
(see 01_example4convergence.py)
"""

u = context.convert_to_ndarray(flow.u_pu)
u_norm = np.linalg.norm(u, axis=0).transpose()
plt.imshow(u_norm)
plt.title('Velocity after simulation')
plt.colorbar()
plt.tight_layout()
plt.show()


================================================
FILE: examples/02_converging_obstacle_flow.py
================================================
import lettuce as lt
import matplotlib.pyplot as plt
import numpy as np
import torch

"""
For descriptions of the initialization, refer to
'01b_first_example_obstacle.py'.

Here, we use a lower Reynolds number for faster convergence.
"""

context = lt.Context(device=torch.device('cuda:0' if torch.cuda.is_available()
                     else 'cpu'), dtype=torch.float32, use_native=False)
nx = 300
ny = 100
Re = 10
Ma = 0.1
lx = 1

flow = lt.Obstacle(context, [nx, ny], reynolds_number=Re, mach_number=Ma,
                   domain_length_x=lx)

x, y = flow.grid
r = .05*y.max()     # radius
x_c = 0.3*x.max()   # center along x
y_c = 0.5*y.max()   # center along y
flow.mask = ((x - x_c) ** 2 + (y - y_c) ** 2) < (r ** 2)

collision = lt.BGKCollision(tau=flow.units.relaxation_parameter_lu)
simulation = lt.Simulation(flow=flow, collision=collision, reporter=[])

simulation.reporter.append(lt.VTKReporter(
    interval=1000,
    filename_base="./data/converging_obstacle"
))

"""
We now add a reporter which we access later. The output can be written to files
specified by out="reporter.txt"
"""
energy = lt.IncompressibleKineticEnergy(flow)
simulation.reporter.append(lt.ObservableReporter(energy, interval=1000,
                                                 out=None))

"""
Now, we do not just run the whole simulation for 30,000 steps, but check the
energy convergence every 2000 steps.
The populations are kept on the GPU until evaluated by [...].cpu()
"""
nmax = 30000
ntest = 1000
it = 0
i = 0
mlups = 0
energy_old = 1
energy_new = 1
while it <= nmax:
    i += 1
    it += ntest
    mlups += simulation(num_steps=ntest)
    energy_new = flow.incompressible_energy().cpu().mean().item()
    print(f"avg MLUPS: {mlups / i:.3f}, avg energy: {energy_new:.8f}, "
          f"rel. diff: {abs(energy_new - energy_old)/energy_old:.8f}")
    if not energy_new == energy_new:
        print("CRASHED!")
        break
    if abs(energy_new - energy_old)/energy_old < 0.0075:
        print(f"CONVERGED! To {abs(energy_new - energy_old)/energy_old:.2%} "
              f"after {it} iterations.")
        break
    energy_old = energy_new
    u = context.convert_to_ndarray(flow.u_pu)
    u_norm = np.linalg.norm(u, axis=0).transpose()
    plt.imshow(u_norm)
    plt.colorbar()
    plt.title(f'Velocities at it={it}')
    plt.show()


================================================
FILE: examples/03_outputs_TGV.py
================================================
import lettuce as lt
import torch
import numpy as np
import matplotlib.pyplot as plt

print("start")

# ---------- Set up simulation -------------
device = torch.device("cuda:0" if torch.cuda.is_available() else "cpu")
context = lt.Context(device=device, dtype=torch.float32)  # single precision
# - torch.float64 for double precision
resolution = 80  # resolution of the lattice, low resolution leads to
# unstable speeds somewhen after 10 (PU)
flow = lt.TaylorGreenVortex(context, resolution, 1600, 0.1, lt.D3Q27)

# select collision model - try also KBCCollision or RegularizedCollision
collision = lt.BGKCollision(tau=flow.units.relaxation_parameter_lu)
simulation = lt.Simulation(flow, collision, [])

# reporters will grab the results in between simulation steps
# (see io.py and simulation.py)
# Output: Column 1: time in LU, Column 2: kinetic energy in PU
energy = lt.IncompressibleKineticEnergy(flow)
kinE_reporter = lt.ObservableReporter(energy, interval=1, out=None)
simulation.reporter.append(kinE_reporter)
# Output: separate VTK-file with ux,uy,uz and p for every time step in ../data
VTKreport = lt.VTKReporter(interval=25, filename_base='./data/tgv')
simulation.reporter.append(VTKreport)

# ---------- Simulate until time = tend (PU) -------------
tend = 10  # [PU]
nend = int(simulation.flow.units.convert_time_to_lu(10))  # [LU]
print(f"Simulating {nend} steps! Maybe drink some water in the meantime.")
# runs simulation, but also returns overall performance in MLUPS (million
# lattice units per second)
print("MLUPS: ", simulation(nend))

# ---------- Plot kinetic energy over time (PU) -------------
# grab output of kinetic energy reporter
E = np.asarray(kinE_reporter.out)
# normalize to size of grid, not always necessary
E[:, 1] = E[:, 1] / (2 * np.pi) ** 3
# save kinetic energy values for later use
np.save("data/TGV3DoutRes" + str(resolution) + "E", E)
fig = plt.figure()
ax1 = plt.subplot(1, 2, 1)
plt.xlabel('Time in physical units')
plt.ylabel('Kinetic energy in physical units')
ax1.plot(simulation.flow.units.convert_time_to_pu(range(0, E.shape[0])),
         E[:, 1])

# ---------- Plot magnitude of speed in slice of 3D volume -------------
# grab u in PU
u = flow.u_pu
# [direction of u: Y, X, Z] (due to ij indexing)
uMagnitude = torch.pow(torch.pow(u[0, :, :, :], 2)
                       + torch.pow(u[1, :, :, :], 2)
                       + torch.pow(u[2, :, :, :], 2), 0.5)
# select slice to plot
uMagnitude = uMagnitude[:, :, round(0.1 * resolution)]
# send selected slice to CPU und numpy, to be able to plot it via matplotlib
uMagnitude = uMagnitude.cpu().numpy()
ax2 = plt.subplot(1, 2, 2)
ax2.matshow(uMagnitude)
plt.tight_layout()
plt.show()
plt.savefig('data/tgv3d-output.pdf')


================================================
FILE: examples/__init__.py
================================================


================================================
FILE: examples/advanced_flows/FailingTGVandObstacle.py
================================================
"""
This file showcases:
 a) interrupting a TGV simulation using a reporter that detects NaN in f
 b) interrupting an obstacle simulation using a reporter that detects Ma > 0.3
"""

import torch
import lettuce as lt
import os

if not os.path.exists("./data"):
    os.mkdir("./data")

### SIMULATION 1: TGV with NaN Reporter###
# a) unstable TGV, that causes NaN values in f, which are detected by the NaN
# ... reporter, who interrupts the simulation.
flow = lt.TaylorGreenVortex(
    lt.Context(dtype=torch.float64),
    resolution=32,
    reynolds_number=30000,
    mach_number=0.3,
    stencil=lt.D2Q9
)
nan_reporter = lt.NaNReporter(100, outdir="./data/nan_reporter",
                              vtk_out=True)
simulation = lt.BreakableSimulation(
    flow=flow,
    collision=lt.BGKCollision(tau=flow.units.relaxation_parameter_lu),
    reporter=[nan_reporter])
simulation(10000)
print(f"Failed after {nan_reporter.failed_iteration} iterations")

### SIMULATION 2: obstacle with High Ma Reporter ###
# b) unstable obstacle flow, that causes high Ma values (Ma > 0.3), which are
# ... detected by the HighMa reporter, who interrupts the simulation.
flow = lt.Obstacle(
    lt.Context(dtype=torch.float64,use_native=False),
    resolution=[32, 32],
    reynolds_number=100,
    mach_number=0.01,
    stencil=lt.D2Q9(),
    domain_length_x=32
)
flow.mask = ((2 < flow.grid[0]) & (flow.grid[0] < 10)
             & (2 < flow.grid[1]) & (flow.grid[1] < 10))
high_ma_reporter = lt.HighMaReporter(100, outdir="./data/highma_reporter",
                                     vtk_out=True)
simulation = lt.BreakableSimulation(
    flow=flow,
    collision=lt.BGKCollision(tau=flow.units.relaxation_parameter_lu),
    reporter=[high_ma_reporter])
simulation(10000)
print(f"Failed after {high_ma_reporter.failed_iteration} iterations")


================================================
FILE: examples/advanced_flows/LidDrivenCavity.ipynb
================================================
{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Lid-driven cavity flow example\n",
    "This is an example of using the cavity flow\n",
    "A two dimensional flow is initialized and simulated. Afterwards, the energy and the velocity field are plotted."
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-08-14T14:45:11.491029Z",
     "start_time": "2024-08-14T14:45:10.421365Z"
    }
   },
   "source": [
    "import lettuce as lt\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import os"
   ],
   "outputs": [],
   "execution_count": 1
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Setup\n",
    "* for running on GPU: device = \"cuda\". CUDA drivers are required!\n",
    "* dtype=torch.float32 for single precision - float64 for double precision\n",
    "* select collision model (here BGKCollision) - try also KBCCollision or RegularizedCollision\n",
    "\n",
    "### Code:\n",
    "* Reporter will grab the results in between simulation steps\n",
    "* Output: Column 1: simulation steps, Column 2: time in LU, Column 3: kinetic energy in PU\n",
    "* Output: separate VTK-file with ux,uy,(uz) and p for every 100. time step in ./output"
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-08-14T14:45:11.922912Z",
     "start_time": "2024-08-14T14:45:11.491874Z"
    }
   },
   "source": [
    "nmax     = 100000\n",
    "nconsole = 1000\n",
    "nreport  = 100\n",
    "epsilon  = 0.0001 # convergence condition: .1 % relative change\n",
    "Re = 100\n",
    "\n",
    "context = lt.Context(use_native=False)\n",
    "flow = lt.Cavity2D(context=context, resolution=64, reynolds_number=Re, mach_number=0.05)\n",
    "simulation = lt.Simulation(flow=flow, collision=lt.KBCCollision(), reporter=[])\n",
    "\n",
    "Energy = lt.IncompressibleKineticEnergy(flow)\n",
    "energy_reporter_internal = lt.ObservableReporter(Energy, interval=nreport, out=None)\n",
    "simulation.reporter.append(energy_reporter_internal)\n",
    "simulation.reporter.append(lt.ObservableReporter(Energy, interval=nconsole)) # print energy\n",
    "if not os.path.isdir(\"data\"):\n",
    "    os.mkdir(\"data\")\n",
    "simulation.reporter.append(lt.VTKReporter(interval=nreport, filename_base=f\"./data/cavity2d_Re{Re}/out\"))"
   ],
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "steps     time     IncompressibleKineticEnergy\n",
      "steps     time     IncompressibleKineticEnergy\n"
     ]
    }
   ],
   "execution_count": 2
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Run simulations"
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-08-14T14:46:07.843211Z",
     "start_time": "2024-08-14T14:45:11.923485Z"
    }
   },
   "source": [
    "energy_new = 0\n",
    "mlups = 0\n",
    "iterations = int(nmax//nconsole)\n",
    "for _ in range(iterations):\n",
    "    energy_old = energy_new\n",
    "    energy_new = Energy(flow.f).mean()\n",
    "    mlups += simulation(nconsole)\n",
    "    if abs((energy_new - energy_old)/energy_new) < epsilon:\n",
    "        print(\"CONVERGENCE! Less than \", epsilon*100, \" % relative change\")\n",
    "        break\n",
    "    if not energy_new == energy_new:\n",
    "        print(\"CRASH\")\n",
    "        break\n",
    "print(\"avg MLUPS: \", mlups/iterations)"
   ],
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 0.0 0.0\n",
      "1000 0.45105489780439517 0.019674744457006454\n",
      "2000 0.9021097956087903 0.02419084496796131\n",
      "3000 1.3531646934131856 0.0268400888890028\n",
      "4000 1.8042195912175807 0.028614206239581108\n",
      "5000 2.255274489021976 0.029889840632677078\n",
      "6000 2.706329386826371 0.030847690999507904\n",
      "7000 3.157384284630766 0.031584933400154114\n",
      "8000 3.6084391824351614 0.0321597158908844\n",
      "9000 4.059494080239556 0.03261049836874008\n",
      "10000 4.510548978043952 0.03296438604593277\n",
      "11000 4.961603875848347 0.03324209898710251\n",
      "12000 5.412658773652742 0.033459488302469254\n",
      "13000 5.863713671457138 0.033629387617111206\n",
      "14000 6.314768569261532 0.03376169875264168\n",
      "15000 6.765823467065927 0.03386494889855385\n",
      "16000 7.216878364870323 0.03394544497132301\n",
      "17000 7.667933262674718 0.03400781750679016\n",
      "18000 8.118988160479113 0.034056372940540314\n",
      "19000 8.570043058283508 0.034093745052814484\n",
      "20000 9.021097956087903 0.034122712910175323\n",
      "21000 9.472152853892299 0.034145306795835495\n",
      "22000 9.923207751696694 0.034162867814302444\n",
      "23000 10.37426264950109 0.03417631983757019\n",
      "24000 10.825317547305485 0.034186627715826035\n",
      "25000 11.27637244510988 0.034194447100162506\n",
      "26000 11.727427342914275 0.03420044109225273\n",
      "27000 12.17848224071867 0.03420506417751312\n",
      "28000 12.629537138523064 0.03420861065387726\n",
      "29000 13.08059203632746 0.03421135991811752\n",
      "30000 13.531646934131855 0.034213364124298096\n",
      "CONVERGENCE! Less than  0.01  % relative change\n",
      "avg MLUPS:  0.6618240655510539\n"
     ]
    }
   ],
   "execution_count": 3
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Post process\n",
    "### Energy Reporter\n",
    "* Grab output of kinetic energy reporter"
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-08-14T14:46:07.920150Z",
     "start_time": "2024-08-14T14:46:07.844066Z"
    }
   },
   "source": [
    "energy = np.array(simulation.reporter[0].out)\n",
    "print(energy.shape)\n",
    "plt.plot(energy[:,1],energy[:,2])\n",
    "plt.title('Kinetic energy')\n",
    "plt.xlabel('Time')\n",
    "plt.ylabel('Energy in physical units')\n",
    "plt.show()"
   ],
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(301, 3)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "execution_count": 4
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Velocity\n",
    "We calculate the speed in Lettuce units depending on the last 'f'. Then we convert this velocity into physical units. For further investigations the tensor must be converted into a Numpy-Array. The norm of the fractions in x and y direction is plotted afterwards."
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-08-14T14:46:08.012981Z",
     "start_time": "2024-08-14T14:46:07.920728Z"
    }
   },
   "source": [
    "u_x, u_y = context.convert_to_ndarray(flow.u_pu)\n",
    "x, y = [context.convert_to_ndarray(_) for _ in flow.grid]\n",
    "plt.quiver(x.T, y.T, u_x.T, u_y.T)"
   ],
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.quiver.Quiver at 0x7f3c654bf260>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ],
      "image/png": "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