Discrete-Maximum-Principle-Preserving Scheme of Two-Phase Flow Model in Porous Medium on Quadrilateral Grid

We construct a maximum-principle-preserving nonlinear scheme to solve the the pressure equation of two phase flow model in porous media on general quadrilateral grid, and a traditional upwind finite volume method to solve the saturation equation. We prove the numerical solution of pressure satisfy the discrete maximum principle. Numerical experiments show that the the numerical pressure and the saturation are without nonphysical oscillation on general quadrilateral grid.