Implement equation representation

badulion / dynabench

MIT License

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Open badulion opened 6 months ago

badulion commented 6 months ago

-> high level API for solvers like PyPde or Dedalus input params

str representation of equation, e.g. "u_t = -c_1u_x - c_2 u_y" or "u_t = -lap(u) + c*grad(u)"
dict of parameters to be used in the equation: in this case c_1, c_2 or c -> can be scalar or field of same shape as grid domain

[not sure yet if those should be included in the equation representation or rather in the solver API:

badulion commented 4 months ago

Still to do:

Add common equations (Burgers, Shallow-Waters, Advection, Diffusion, Kuramotosivashinsky, Reaction-Diffusion, Brusselator,. ...)
Add Initial conditions from literature
Related Work on Equations used in Papers
Add simplification of equations to expressions of u_x, u_y, u_xx,...