Multiscale FEM Solution and Boundary Interactions of water in heterogeneous porous media

A heterogeneous multi-scale rationalized method (HMM) implemented in FEM has been introduced as a general framework for the numerical computation of solutions to coupled problems with multiple scales. The main objective of this research is to avoid the computation CPU time length upon the need of fine scale of a few meter size elements up to kilometers dimensions upon shape functions as well as of the coefficients of the homogenized equation. In a general FE framework, to solve coupled problems, this method discretizes the physical problem directly by different scaled meshes of macroscopic FEM model which does not (and cannot) resolve the fine scales of the solution. Derivations of heterogeneous multi-scales through homogenized equations upon the correct micro-scale behavior including the correct interaction of domains from the known macroscopic solution are the major tasks.

Keywords:

multi-scale , macroscopic , coupled , micro scale , heterogeneous