A high order finite difference method with Richardsonextrapolation for 3D convection diffusion equation
A high order finite difference method with Richardsonextrapolation for 3D convection diffusion equation
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DOI：
10.1016/j.amc.2009.10.035
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发表时间：
2010
期刊：
影响因子：
--
通讯作者：
Y. Ma;Y. Ge
中科院分区：
文献类型：
--
作者：
Y. Ma;Y. Ge
本文将Sun和Zhang [24]关于一维和二维定常对流扩散方程的基于Richardson外推技术和算子插值格式的高阶有限差分方法推广到三维情形。首先，我们采用四阶紧致差分格式在细网格和粗网格上得到四阶精度的解。然后，我们使用Richardson外推技术，将两个近似解结合起来，得到粗网格上的六阶精确解。最后，我们采用算子插值方法在细网格上获得了六阶精度的解。在此过程中，我们使用交替方向隐式（ADI）方法来解决所产生的线性方程组。数值实验验证了该方法的准确性和有效性。
In this paper, we extend the Sun and Zhang’s [24] work on high order finite difference method, which is based on the Richardson extrapolation technique and an operator interpolation scheme for the one and two dimensional steady convection diffusion equations to the three dimensional case. Firstly, we employ a fourth order compact difference scheme to get the fourth order accurate solution on the fine and the coarse grids. Then, we use the Richardson extrapolation technique by combining the two approximate solutions to get a sixth order accurate solution on coarse grid. Finally, we apply an operator interpolation scheme to achieve the sixth order accurate solution on the fine grid. During this process, we use alternating direction implicit (ADI) method to solve the resulting linear systems. Numerical experiments are conducted to verify the accuracy and effectiveness of the present method.