A Moving Mesh Finite Difference Method for Non-Monotone Solutions of Non-Equilibrium Equations in Porous Media. (28th July 2017)

• Record Type: Journal Article
• Authors: Zhang, Hong; Zegeling, Paul Andries
• Is Part Of: Communications in computational physics. Volume 22:Number 4(2017:Oct.)
• Page Start: 935
• Page End: 964
• Publication Date: 2017-07-28
• Subjects: 35C07, -- 35Q35, -- 65M50, -- 74S20, -- 76S05; Relaxation non-equilibrium Richards equation, -- modified Buckley-Leverett equation, -- saturation overshoot, -- traveling wave analysis, -- moving mesh finite difference method; Mathematical physics -- Data processing -- Periodicals; Physics -- Data processing -- Periodicals; 530.150285
• DOI: 10.4208/cicp.OA-2016-0220
• Languages: English
• ISSNs: 1815-2406

Abstract

Abstract: An adaptive moving mesh finite difference method is presented to solve two types of equations with dynamic capillary pressure effect in porous media. One is the non-equilibrium Richards Equation and the other is the modified Buckley-Leverett equation. The governing equations are discretized with an adaptive moving mesh finite difference method in the space direction and an implicit-explicit method in the time direction. In order to obtain high quality meshes, an adaptive monitor function with directional control is applied to redistribute the mesh grid in every time step, then a diffusive mechanism is used to smooth the monitor function. The behaviors of the central difference flux, the standard local Lax-Friedrich flux and the local Lax-Friedrich flux with reconstruction are investigated by solving a 1D modified Buckley-Leverett equation. With the moving mesh technique, good mesh quality and high numerical accuracy are obtained. A collection of one-dimensional and two-dimensional numerical experiments is presented to demonstrate the accuracy and effectiveness of the proposed method.