Three-dimensional multi-material polyhedral method for diffusion

For Inertial Confinement Fusion simulations the diffusion of energy at material boundaries is an important physical process. To model this we present a three dimensional finite volume multi-material scheme based on the construction of an unstructured supermesh from a non-aligned base mesh. In this paper we will use a surrogate supermesh based on local adjustments to the supermesh. In this paper numerical results are shown for planar and cylindrical test problems on non-aligned meshes. It will be shown that the multi-material scheme produces superior results over a simplier homogenised scheme. It will also be shown that the new scheme has close to optimal convergence properties while the homogenised scheme performs poorly.