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非结构四面体网格上三维非线性扩散方程的有限体积法
引用本文:殷东生,杜正平,陆金甫.非结构四面体网格上三维非线性扩散方程的有限体积法[J].清华大学学报(自然科学版),2005(9).
作者姓名:殷东生  杜正平  陆金甫
作者单位:清华大学数学科学系 北京100084 (殷东生,杜正平),清华大学数学科学系 北京100084(陆金甫)
基金项目: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:为了有效地数值模拟科学和工程中有广泛应用的非线性扩散方程,在三维线性扩散方程非结构四面体网格的有限体积法的基础上,提出了一个计算非结构四面体网格上非线性扩散方程的有限体积法。方法采用网格单元中心作为计算节点,相对于网格点的方法,计算量减少了一半。用L agrange因子法得到网格点上的值,考虑了网格中心点和网格点的相对位置,更适应大变形的网格。利用算子分裂,使计算更加简单。用N ew ton-B iCG STAB法来求解得到非线性方程组。数值结果表明:该方法具有二阶精度、保持通量守恒、对大变形的网格适应性强。

关 键 词:有限体积法  三维非线性扩散方程  非结构四面体网格  Newton迭代法

Finite volume scheme for 3-D nonlinear diffusion equations on unstructured tetrahedral meshes
YIN Dongsheng,DU Zhengping,LU Jinfu.Finite volume scheme for 3-D nonlinear diffusion equations on unstructured tetrahedral meshes[J].Journal of Tsinghua University(Science and Technology),2005(9).
Authors:YIN Dongsheng  DU Zhengping  LU Jinfu
Abstract:3-D nonlinear diffusion equations occur in various fields such as heat transfer, fluid dynamics, astrophysics, and finance. The finite volume method for linear 3-D diffusion equations on unstructured tetrahedral grids was modified to create a finite volume method for 3-D nonlinear diffusion equations on unstructured tetrahedron meshes. Flux conservation was used to get the computational solutions. So the scheme is second-order and flux conservative. The cell-center approximation reduces the number of computations. The Lagrangian multiplier method makes the method more suitable for unstructured grids with the splitting method used to reduce computational costs. The Newton-BiCGSTAB method is used to solve the equations derived from the finite volume scheme. The numerical results show that the method is fast and effective.
Keywords:finite volume method  3-D nonlinear diffusion equations  unstructured tetrahedral meshes  Newton iterative method
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