【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。更多还原

【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.更多还原