MONOTONICITY CORRECTIONS FOR NINE-POINT SCHEME OF DIFFUSION EQUATIONS  

作　　者：Wang Kong Zhenying Hong Guangwei Yuan Zhiqiang Sheng 

机构地区：[1]School of Mathematics,Nanjing University of Aeronautics and Astronautics,Nanjing 211106,China [2]Key Laboratory of Mathematical Modelling and High Performance Computing of Air Vehicles(NUAA),MIIT,Nanjing 211106,China [3]Laboratory of Computational Physics,Institute of Applied Physics and Computational Mathematics,Beijing 100088,China [4]HEDPS,Center for Applied Physics and Technology,Peking University,Beijing 100871,China

出　　处：《Journal of Computational Mathematics》2024年第5期1305-1327,共23页计算数学（英文）

基　　金：supported by the National Natural Science Foundation of China(Grant Nos.12071045,12201299);the Natural Science Foundation of Jiangsu Province(Grant No.BK20220870);the Youth Foundation of Laboratory of Computational Physics(Grant No.HX02021-37).

摘　　要：In this paper,we present a nonlinear correction technique to modify the nine-point scheme proposed in[SIAM J.Sci.Comput.,30:3(2008),1341-1361]such that the resulted scheme preserves the positivity.We first express the flux by the cell-centered unknowns and edge unknowns based on the stencil of the nine-point scheme.Then,we use a nonlinear combination technique to get a monotone scheme.In order to obtain a cell-centered finite volume scheme,we need to use the cell-centered unknowns to locally approximate the auxiliary unknowns.We present a new method to approximate the auxiliary unknowns by using the idea of an improved multi-points flux approximation.The numerical results show that the new proposed scheme is robust,can handle some distorted grids that some existing finite volume schemes could not handle,and has higher numerical accuracy than some existing positivity-preserving finite volume schemes.

关 键 词：Monotonicity corrections Diffusion equation Improved MPFA Distorted meshes 

分 类 号：O17[理学—数学]