Numerical Convergence of the MPFA O-Method for General Quadrilateral Grids in Two and Three Dimensions
Numerical Convergence of the MPFA O-Method for General Quadrilateral Grids in Two and Three Dimensions
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二维和三维一般四边形网格MPFA O方法的数值收敛
DOI：
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发表时间：
2006
期刊：
影响因子：
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通讯作者：
R. A. Klausen
中科院分区：
文献类型：
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作者：
I. Aavatsmark;G. T. Eigestad;R. A. Klausen
本文给出了四边形网格的MPFA O法，并给出了位势速度和法向速度的收敛速度。通过数值实验估计了算法的收敛速度。当势函数为H1+α，α>；0时，在物理空间中的粗网格上找到的L 2收敛级数分别为势函数min{2，2α}和法向速度函数min{1，α}。对于光滑网格，法向速度的收敛阶增加到Min{2，α}。对于粗糙网格上的均匀流，O-方法是精确的。这也适用于三维空间，细胞可能具有非平面表面。
This paper presents the MPFA O-method for quadrilateral grids, and gives convergence rates for the potential and the normal velocities. The convergence rates are estimated from numerical experiments. If the potential is in H 1+α , α>0, the found L 2 convergence order on rough grids in physical space is min{2, 2α} for the potential and min{1, α} for the normal velocities. For smooth grids the convergence order for the normal velocities increases to min{2,α}. The O-method is exact for uniform flow on rough grids. This also holds in three dimensions, where the cells may have nonplanar surfaces.