A Moving Mesh Finite Difference Method for Non-Monotone Solutions of Non-Equilibrium Equations in Porous Media (Communications in Computational Physics, 2017)
An adaptive moving mesh finite difference method is presented to solvetwo types of equations with dynamic capillary pressure effect in porous media. One isthe non-equilibrium Richards Equation and the other is the modified Buckley-Leverettequation. The governing equations are discretized with an adaptive moving mesh finite difference method in the space direction and an implicit-explicit method in thetime direction. In order to obtain high quality meshes, an adaptive monitor functionwith 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 behaviorsof the central difference flux, the standard local Lax-Friedrich flux and the local Lax-Friedrichflux with reconstruction are investigated by solving a 1D modified Buckley-Leverettequation. With the moving mesh technique, good mesh quality and high numericalaccuracy are obtained. A collection of one-dimensional and two-dimensionalnumerical experiments is presented to demonstrate the accuracy and effectiveness ofthe proposed method.
Keywords: 65M06; 76D05; 74F10; 92C10