A Combination Method of Mixed Multiscale Finite-Element and Laplace Transform for Flow in a Dual-Permeability System

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. T...

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Bibliographic Details
Published in:ISRN applied mathematics 2012-01, Vol.2012 (2012), p.1-10
Main Authors: Liu, Tang-Wei, Xu, He-Hua, Qiu, Xue-Lin
Format: Article
Language:English
Subjects:
Applied mathematics
Approximation
Basis functions
Boundary conditions
Finite element analysis
Finite element method
Finite volume method
Heterogeneity
Laplace transforms
Mathematical analysis
Mathematical models
Numerical analysis
Partial differential equations
Permeability
Studies
Transforms
Velocity
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Summary: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.
ISSN:2090-5564
2090-5572
2090-5572
DOI:10.5402/2012/202893