A time-independent solver for diffusive transport in 2D eroded geometries

To describe diffusive transport of quantities such as heat or chemical concentrations in porous media, the diffusion equation must be solved in complex unbounded geometries. I will describe a numerical method that uses the Laplace transform to recast the time-dependent diffusion equation into a series of time-independent PDEs. These elliptic PDEs are solved using a boundary integral equation method, and the Laplace transform is inverted by carefully choosing a well-behaved Bromwich integral. By combining these techniques, high-order accuracy in both space and time are achieved. I will use this method to study the effects of erosion on diffusive processes.