A moment-of-fluid method for diffusion equations on irregular domains in multi-material systems*

A new numerical method is developed for the solution of the diffusion problem in a system of several materials.  In such a system, the diffusion coefficients are piecewise continuous and jumps in their values can occur across the complex-shaped interfaces between contiguous materials. A moment-of-fluid procedure is employed to re-construct the interfaces. This procedure enables accurate reconstruction of any number of material interfaces in a computational cell. Furthermore, it is capable of capturing thin filamentary regions without the necessity of adaptive mesh refinement. It is demonstrated in a simple canonical case. It has the potential to enable numerical simulation of complex flows of technological importance relevant to materials and manufacturing processes, in that it can capture multiple phase changes that occur in such flows in complex domains.