So I'm trying to implement a 9-point stencil discretization to the 2D difussion equation. The stencil is here.However, most of the literature deals with a Laplacian that has a constant diffusion coefficient. i.e.$$ f_t=d\Delta f(x,y). $$However the problem I'm dealing with has a variable diffusion coefficient, i.e.$$ f_t=\nabla\cdot (d(x,y)\nabla f(x,y)). $$How would you implement that in a 9-point stencil? I've seen in the literature the 5-point stencil version for variable coefficient but not the 9-point one.
9-point stencil finite difference Laplacian with variable diffusion coefficients
finite difference;fluid dynamics;advection diffusion;diffusion