Multiscale Computation of Fluid Flow in Heterogeneous Media

Abstract

There are many interesting physical problems that have multiscale solutions. These problems range from composite materials to wave propagation in random media, flow and transport through heterogeneous porous media, and turbulent flow. Computing these multiple scale solutions accurately presents a major challenge due to the wide range of scales in the solution. It is very expensive to resolve all the small scale features on a fine grid by direct num-erical simulations. A natural question is if it is possible to develop a multiscale computational method that captures the effect of small scales on the large scales using a coarse grid, but does not require resolving all the small scale features. Such multiscale method can offer significant computational savings.