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arXiv · 1611.08553

A moving mesh finite difference method for non-monotone solutions of non-equilibrium equations in porous media

Hong Zhang·Paul Andries Zegeling
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Abstract

An adaptive moving mesh finite difference method is presented to solve two types of equations with dynamic capillary pressure term 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 time-dependent monitor function with directional control is applied to redistribute the mesh grid in every time step, and 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.

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Hong Zhang, Paul Andries Zegeling. 2016-11-25. A moving mesh finite difference method for non-monotone solutions of non-equilibrium equations in porous media. https://doi.org/10.4208/cicp.oa-2016-0220

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