A Hybrid Laplace Transform Mixed Multiscale Finite-Element Method for Flow Model in Porous Media

摘要

This paper presents a hybrid Laplace transform Mixed Multiscale Finite-element Method (MMsFEM) to solve partial differential equations of flow in porous media. First, the time term of parabolic equation with unknown pressure term is removed by the Laplace transform. Then, to obtain the numerical approximation of pressure and velocity directly, the transformed equations on coarse mesh are solved by mixed multiscale FEM, which utilizes the effects of fine-scale heterogeneities through basis function formulations computed from local flow problems. Finally, the associated pressure and velocity transform are inverted by the method of numerical inversion of the Laplace transform to obtain the numerical solution.