A high‐order finite difference discretization strategy based on extrapolation for convection diffusion equations
A high‐order finite difference discretization strategy based on extrapolation for convection diffusion equations
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DOI：
10.1002/num.10075
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发表时间：
2004-01
影响因子：
3.9
通讯作者：
Hai-wei Sun;Jun Zhang
中科院分区：
文献类型：
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作者：
Hai-wei Sun;Jun Zhang
本文提出了一种新的高阶有限差分离散策略，该策略基于Richardson外推技术和算子插值格式，求解对流扩散方程.对于特定的实现，我们通过使用四阶紧致差分格式来求解细网格方程和粗网格方程。然后，我们将两个近似解结合起来，并使用Richardson外推来计算六阶精度的粗网格解。通过使用算子插值方案对六阶粗网格解进行插值，获得六阶精度细网格解。数值结果表明，所提出的有限差分离散策略的精度和有效性，相比六阶组合紧致差分（CCD）格式，和标准的四阶紧致差分（FOC）格式。© 2003 Wiley Periodicals，Inc. Numer Methods Partial Differential Eq 20：18-32，2004.
We propose a new high‐order finite difference discretization strategy, which is based on the Richardson extrapolation technique and an operator interpolation scheme, to solve convection diffusion equations. For a particular implementation, we solve a fine grid equation and a coarse grid equation by using a fourth‐order compact difference scheme. Then we combine the two approximate solutions and use the Richardson extrapolation to compute a sixth‐order accuracy coarse grid solution. A sixth‐order accuracy fine grid solution is obtained by interpolating the sixth‐order coarse grid solution using an operator interpolation scheme. Numerical results are presented to demonstrate the accuracy and efficacy of the proposed finite difference discretization strategy, compared to the sixth‐order combined compact difference (CCD) scheme, and the standard fourth‐order compact difference (FOC) scheme. © 2003 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 20: 18–32, 2004.