Some Methods To Eliminate The Cell-vertex Unknowns In The Construction Of Monotone Finite Volume Scheme For Three-dimensional Diffusion Equations

In this paper,we mainly study the application of diffenent methods to eliminate cell-vertex unknowns in the construction of monotone finite volume scheme for three-dimensional diffusion equations.Firstly,the cell-centered finite volume scheme is established on the tetra-hedral meshes,the resulting scheme has only cell-centered unknowns,and pre-serve monotone.In the process of deducing the scheme,the resulting discrete flux contains not only cell-centered unknowns,but also cell-vertex unknowns.In order to get the scheme that only has cell-centered unknowns,we must e-liminate cell-vertex unknowns.The inverse distance weighted method,Taylor method and ?-Taylor method are discussed in this paper.The inverse distance weighted method does not have convergent order,the Taylor method and the?-Taylor method are only suitable for the smooth diffusion coefficient prob-lems.So a new method,which is called vertex-moving method,is introduced in this paper.In view of continuous diffusion coefficient and discontinuous diffusion coefficient,we gave some numerical examples on uniform,distorted and g-mesh tetrahedral meshes respectively with different methods.And the numerical results show that the scheme which uses vertex-moving method is robust and effective.The main points of this paper are that a new method,which is called vertex-moving method,is introduced to eliminate cell-vertex unknowns.Vertex-moving method is to approximate the normal flux on cell-vertex by the normal flux on the point in the segment which is connected cell-vertex and cell-center.