非正规四边形网格二维抛物方程的有限体积差分方法  

NONORTHOGONAL QUADRILATERAL MESH FINITE VOLUME DIFFERENCE METHOD OF 2-D DIFFUSION EQUATION

作　　者：杜正平[1] 殷东生[1] 刘晓遇[1] 陆金甫[1] 

机构地区：[1]清华大学数学科学系,北京100084

出　　处：《数值计算与计算机应用》2004年第2期138-144,共7页Journal on Numerical Methods and Computer Applications

基　　金：国家自然科学基金(10176023);国防科技重点实验室基金试点项目(0076.8.10110)

摘　　要：A new finite volume difference method for solving 2-D diffusion equation isconstructcd in this paper. The choice of computational nodes is studied on thegross distortion concave quadrilateral grid. We choose the midpoint of a diagonalline of the mesh cells as the calculation nodes because it can assure the cells con-tain the calculation nodes and reduce the total calculation. In order to keep theconservation, we use the conditions of flux conservation to compute the values ofthe central of the boundary. Lagrange multiplier method is used to get the valuesof grid points. With the consideration of the relative position of the grid points,the method is more suitable for nonorthogonal grids. We make experiments onconcave grids and "Z" grids. The numerical results show that the new arithmeticis feasible and effective, especially for highly distortional meshes.A new finite volume difference method for solving 2-D diffusion equation isconstructcd in this paper. The choice of computational nodes is studied on thegross distortion concave quadrilateral grid. We choose the midpoint of a diagonalline of the mesh cells as the calculation nodes because it can assure the cells con-tain the calculation nodes and reduce the total calculation. In order to keep theconservation, we use the conditions of flux conservation to compute the values ofthe central of the boundary. Lagrange multiplier method is used to get the valuesof grid points. With the consideration of the relative position of the grid points,the method is more suitable for nonorthogonal grids. We make experiments onconcave grids and 'Z' grids. The numerical results show that the new arithmeticis feasible and effective, especially for highly distortional meshes.

关 键 词：扩散方程 数值模拟 流体力学 数值热传导 

分 类 号：O351[理学—流体力学]