Multiscale iterative methods, coarse level operator construction and discrete homogenization techniques
Michael Griebel · OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information) · 1996
For problems which model locally strong varying phenomena on a micro-scale level, the grid for numerical simulation can not be chosen sufficiently fine enough due to reasons of storage requirements and numerical complexity. A typical example for such kind of a problem is the diffusion equation with strongly varying diffusion coefficients as it arises as Darcy law in reservoir simulation and related problems for flow in porous media. Therefore, on the macro-scale level, it is necessary to work with averaged equations which describe directly the large-scale behavior of the problem under consideration. In the numerical simulation of reservoir performance this is achieved e.g. by renormalization or homogenization, as simpler approaches like the arithmetic, geometric or harmonic mean turn out to be invalid for systems with strong permeability variations.