三维扩散方程非正交六面体网格的有限体积差分法  

Nonorthogonal hexahedral mesh finite volume difference method for the 3-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：《清华大学学报（自然科学版）》2003年第10期1365-1368,共4页Journal of Tsinghua University(Science and Technology)

基　　金：国家自然科学基金资助项目(10176023);国防科技重点实验室基金试点项目(00JS76.8.1JW0110)

摘　　要：三维扩散方程非正交网格的差分方法是计算流体力学和数值热传导中一个基础性的课题。该文在二维扩散方程的有限体积差分方法的基础上,研究了在非正交六面体网格下三维扩散方程的有限体积差分方法,提出了一个计算精度很高、通量守恒且适应大变形网格的有限体积差分格式。取单元中心作为计算节点,减小了计算量;利用通量守恒条件确定界面中心的函数值,保证方法的守恒性;对网格点采用了Lagrange因子插值法,考虑了各插值点的相对位置,因此更适应非正交网格的计算;采用不完全三角分解预处理Bi-CGSTAB方法求解线性代数方程组。不同Z网格上的数值实验结果表明该算法是有效的。Accurate nonorthogonal mesh difference methods for the 3D diffusion equation for scientific computations are a fundamental problem in computational fluid dynamics (CFD) and numerical heat conduction analyses. Based on the finite volume difference method for the 2D diffusion equation, a finite volume difference method was developed for the 3D diffusion equation for nonorthogonal meshes which is accurate, can conserve the fluxes and is suitable for highly distorted grids. The method uses cellcenter nodes, which reduces computations of the cell volumes and vectors and, hence, the entire computational lood. To conserve the fluxes, flux conservation was used to compute the fluxes at the center of the interfaces. The Lagrange method was used to interpolate the values of the dependent variables from the grid points. Since the interpolation accounts for the relative positions of the grid points, the method is more suitable for nonorthogonal grids. Lowerupper triangular factorization preconditioning was used with the BiCGSTAB method to solve the linear algebra equations. Experiments on 'Z' grids show that the method is accurate and very effective on various grids with different geometric measures and distortions. 

关 键 词：三维扩散方程 非正交六面体网格 有限体积差分法 Lagrange因子插值法 三维抛物方程 

分 类 号：O175.29[理学—数学] O241.82[理学—基础数学]