A Combination Method of Mixed Multiscale Finite-Element and Laplace Transform for Flow in a Dual-Permeability System. (30th July 2012)

• Record Type: Journal Article
• Authors: Liu, Tang-Wei; Xu, He-Hua; Qiu, Xue-Lin
• Other Names: Du H. Academic Editor.; Kyriacou G. Academic Editor.
• Is Part Of: ISRN applied mathematics. Volume 2012(2012)
• Publication Date: 2012-07-30
• Subjects: Mathematics -- Periodicals; Mathematics; Periodicals; Electronic journals; 510
• DOI: 10.5402/2012/202893
• Languages: English
• ISSNs: 2090-5564

Abstract

Abstract : An efficient combination method of Laplace transform and mixed multiscale finite-element method for coupling partial differential equations of flow in a dual-permeability system is present. First, the time terms of parabolic equation with unknown pressure term are removed by the Laplace transform. Then the transformed equations are solved by mixed FEMs which can provide the numerical approximation formulas for pressure and velocity at the same time. With some assumptions, the multiscale basis functions are constructed by utilizing the effects of fine-scale heterogeneities through basis functions formulation computed from local flow problems. Without time step in discrete process, the present method is efficient when solving spatial discrete problems. At last, the associated pressure transform is inverted by the method of numerical inversion of the Laplace transform.