Finite difference method on curvilinear grid

Introduction

Curvilinear_Grid_FDM is project that implement finite difference method on curvilinear grid. The code can be modifide easily by students interested in this topic. More features will be added in the future.

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Brief theoretical description

TBD

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Program Structure

CUR_GRID_FDM/DiscreteSchemes

There two modules provide necessary informations to assemble discrete schemes.

• CalCoeff.py

  Calculate essential coefficients for curvilinear coordinates. A structure mesh is given for computing the coefficients. The available information inlcudes: covariant basis vector, contravariant basis vector, metric tensor and christoffel symbols.

• OperatorFDM3D.py

  Genertate the coefficient matrix for 3D finite difference computation. A structure mesh is given for querying the coefficients. The coefficient matrix can be obtained with several kinds of derivative operations.

CUR_GRID_FDM/Geometry

Provide the information of a structure mesh.

• RectangularMesh.py

  Provide a structural rectangular mesh.

• CurveRectangularMesh.py

  Provide a structural curve rectangular mesh.

• DonutMesh.py

  Provide a structural donut mesh.

Solver

The different solvers that need to be built by the user under specific scenario.

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Example

LAPLACE equation

Laplace equation is solved in a (1) rectangular, (1) curved rectangular and (3) cylindrical domain with dirichlet boundary conditions on all sides.

TODO

1. Support user defined mesh.

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References

[1] Finite Difference Coefficients Calculator