Research On Nine-point Scheme Of Diffusion Equation And Auxiliary Unknown Interpolation Algorithm

In this paper,we study the nine point scheme of diffusion equation.First,we in-vestigate the interpolation algorithm of auxiliary unknowns in the finite volume scheme for diffusion problems.On this basis,we summarize the properties that a good interpo-lation algorithm should have and whether the existing algorithms meet these properties.Then,the numerical barrier issue encountered in solving a class of strongly nonlinear parabolic problems is addressed and the reasons for this phenomenon are analyzed.To solve this problem,an improved nine point scheme is proposed.Numerical examples show that the improved scheme can overcome this problem effectively.At last,under linearity preserving criterion,a new vertex interpolation algorithm,which is called the linearity-preserving limit weight,is constructed by using of the MPFA interpolation and a special limit technique.The new algorithm can be applied to arbitrary grids and anisotropic diffusion problems equipped with any discontinuous coefficients.More-over,it can be easily extended to 3D grids.From numerical examples,one can find that the solution and the flux can achieve desired accuracy using nine point scheme with linearity-preserving limit weight.