Forward Euler method for solving PDE's in CompuCell3D.
Remark: we present more complete derivations of explicit finite difference scheme for diffusion solver in “Introduction to Hexagonal Lattices in CompuCell3D”.
In CompuCell3D most of the solvers uses explicit schemes (Forward Euler method) to obtain PDE solutions. Thus for the diffusion equation we have:
In a discretetized form we may write:
where to save space we used shorthand notation:
and similarly for other coordinates.
After rearranging terms we get the following expression:
where the sum over index 'i' goes over neighbors of point (x,y,z) and the neighbors will have the following concentrations: , ,…, .
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