Solution of the diffusion equation in multi‐material domains by sub‐division of elements along reconstructed interfaces

This paper describes the accurate solution of the diffusion equation in three-dimensional multi-material domains where some mesh elements contain more than one material. Given the volume fractions of each material in mesh elements, the method first recreates the material interfaces in the elements using interface reconstruction methods. Then the mesh is subdivided along the interfaces making sure that the final polyhedral mesh is conforming. Finally, the diffusion equation is solved on the sub-divided mesh containing all single material elements. It is shown that the method produces second-order accurate solutions with a lower error than methods that average the material properties in the multi-material elements. Published in 2010 by John Wiley & Sons, Ltd.