pyapes: PYthon Awesome Partial differential Equation Solver (general purpose finite difference PDE solver)

Description

pyapes is designed to solve various engineering problems in rectangular grid.

The goal of pyapes (should be/have) is

• Cross-platform
  • Both tested on Mac and Linux (Arch)
  • Windows support is under testing
• GPU acceleration in a structured grid with PyTorch
  • Use of torch.Tensor. User can choose either torch.device("cpu") or torch.device("cuda").
• Generically expressed (OpenFOAM-like, human-readable formulation)

Installation

We recommend to use poetry to manage/install all dependencies.

• From git

  git clone git@gitlab.ethz.ch:kchung/pyapes.git
  cd pyapes
  poetry install

• From pypi

  python3 -m pip install pyapes
  # or
  poetry add pyapes

Dependencies

• Core dependency
  • python >= 3.10
  • As of 19.02.2023, torch does not support 3.11 properly (for the official release). Therefore, stick to python3.10.
  • torch >= 1.10.0
• Dependencies from my personal projects
  • pymyplot (plotting tools)
  • pymytools (misc. tools including data I/O, logging, etc.)

Implemented Features

• CPU/GPU(CUDA) computation using torch

• (OpenFOAM like) generically expressed solver

  >>> solver.set_eq(fdm.laplacian(1.0, var) == rhs)
  >>> solver.solve()

• FDM Discretizations

  • Spatial: Grad, Laplacian, Div
  • Supports flux limiter upwind for the Div operator
  • Temporal: Ddt

• Boundary conditions:

  • Supports Dirichlet, Neumann, Periodic, and Symmetry

• Demo cases in jupter notebooks

Examples

Check our demos files

Todos

• Boundary conditions
  • [ ] Inflow/Outflow
• Need different derivative order at the cell face
  • Additional features
  • [ ] High order time discretization
  • [ ] Immersed body BC
  • [ ] Higher order flux limiters (quick)
• Testing and validation
  • [ ] Ddt class (implementation is tested but haven't validated with practical test cases)
• Working on demo files
  • [x] The Poisson equation
  • [x] The advection-diffusion equation
  • [ ] The Burgers' equation
  • [ ] The Navier-Stokes equation at low Reynolds numbers
  • [ ] The Black-Scholes equation