Jonathan E. Guyer, Daniel Wheeler, James A. Warren
We present an object oriented partial differential equation (PDE) solver written in Python based on a standard finite volume (FV) approach.The solution of coupled sets of PDEs is ubuquitous in the numerical simulation of science problems. Numerous PDE solvers exist using a variety of languages and numerical approaches. many are proprietary, expensive and difficult to customize. As a result, scientists spend considerable resources repeatedly developing limited tools for specific problems. Our approach, combining the FV method and Python, provides a tool that is extensible, powerful and freely available. A significiant advantage to Python is the existing suite of tools for array calculations. sparse matrices and data representation.Our framework includes terms for transient diffusion. convection and standard sources, enabling the solution of arbitrary combinations of coupled elliptic, hyperbolic and parabolic PDE's. Current models include phase field treatments of electrochemical, polycrystalline and dendritic phase transformations.Movitation: Existing approaches, Weaknesses of existing approaches.Approach: Object relationships between variables, equations, terms, etc. Python/is/the input file, Leverage 3rd party numeric libraries.Drawbacks: Efficiency, Complexity of installation.Examples: Crystal Growth, Thermodynamics of Stressed Solids, and Electrochemistry.
March 24-26, 2004
To Be Determined
finite volume, partial differential eq., phase field
, Wheeler, D.
and Warren, J.
A Finite Volume PDE Solver Using Python (FiPy), PyCON 2004, Undefined
(Accessed December 1, 2023)