标题：A Block-Centered Finite Difference Method for Slightly Compressible Darcy-Forchheimer Flow in Porous Media
作者：Rui, Hongxing; Pan, Hao
作者机构：[Rui, Hongxing] Shandong Univ, Sch Math, Jinan 250100, Shandong, Peoples R China.; [Pan, Hao] Shandong Agr Univ, Sch Informat Sci & Engn, Tai An 271 更多
通讯作者地址：[Rui, HX]Shandong Univ, Sch Math, Jinan 250100, Shandong, Peoples R China.
来源：JOURNAL OF SCIENTIFIC COMPUTING
关键词：Block-centered finite difference; Darcy-Forchheimer flow; Compressible;; Error estimate; Numerical experiment
摘要：A block-centered finite difference method is introduced to solve an initial and boundary value problem for a nonlinear parabolic equation to model the slightly compressible flow in porous media, in which the velocity-pressure relation is described by Darcy-Forchheimer's Law. The method can be thought as the lowest order Raviart-Thomas mixed element method with proper quadrature formulation. By using the method the velocity and pressure can be approximated simultaneously. We established the second-order error estimates for pressure and velocity in proper discrete norms on non-uniform rectangular grid. No time-step restriction is needed for the error estimates. The numerical experiments using the scheme show that the convergence rates of the method are in agreement with the theoretical analysis.