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Volume 22, Issue 4
A Moving Mesh Finite Difference Method for Non-Monotone Solutions of Non-Equilibrium Equations in Porous Media

Hong Zhang & Paul Andries Zegeling

DOI: Vol. 22, No. 4, pp. 913-934

Commun. Comput. Phys., 22 (2017), pp. 935-964.

Published online: 2017-10

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  • 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.

  • Keywords

65M06 76D05 74F10 92C10

  • AMS Subject Headings

Moving least squares immersed boundary method direct-forcing method NavierStokes equations cell sorting device

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COPYRIGHT: © Global Science Press

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@Article{CiCP-22-935, author = {Hong Zhang and Paul Andries Zegeling}, title = {A Moving Mesh Finite Difference Method for Non-Monotone Solutions of Non-Equilibrium Equations in Porous Media}, journal = {Communications in Computational Physics}, year = {2017}, volume = {22}, number = {4}, pages = {935--964}, 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.

}, issn = {1991-7120}, doi = {https://doi.org/Vol. 22, No. 4, pp. 913-934}, url = {http://global-sci.org/intro/article_detail/cicp/9988.html} }
TY - JOUR T1 - A Moving Mesh Finite Difference Method for Non-Monotone Solutions of Non-Equilibrium Equations in Porous Media AU - Hong Zhang & Paul Andries Zegeling JO - Communications in Computational Physics VL - 4 SP - 935 EP - 964 PY - 2017 DA - 2017/10 SN - 22 DO - http://doi.org/Vol. 22, No. 4, pp. 913-934 UR - https://global-sci.org/intro/article_detail/cicp/9988.html KW - 65M06 KW - 76D05 KW - 74F10 KW - 92C10 AB -

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.

Hong Zhang and Paul Andries Zegeling. (2017). A Moving Mesh Finite Difference Method for Non-Monotone Solutions of Non-Equilibrium Equations in Porous Media. Communications in Computational Physics. 22 (4). 935-964. doi:Vol. 22, No. 4, pp. 913-934
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