A Family of Fourth-Order and Sixth-Order Compact Difference Schemes for the Three-Dimensional Poisson Equation
A Family of Fourth-Order and Sixth-Order Compact Difference Schemes for the Three-Dimensional Poisson Equation
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DOI：
10.1007/s10915-012-9607-6
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发表时间：
2012-05
影响因子：
2.5
通讯作者：
S. Zhai;Xinlong Feng;Yinnian He
中科院分区：
文献类型：
--
作者：
S. Zhai;Xinlong Feng;Yinnian He
本文详细推导了三维线性Poisson方程的四阶和六阶紧致差分格式。利用有限体积法(FV)进行推导，得到了基于两种不同类型的对偶划分的最高阶紧致格式。此外，还得到了一种新的四阶紧致格式，数值实验表明，新格式比其他已知的四阶格式要好得多。并给出了非线性问题的提纲。数值实验验证了这种新方法的可行性和这种四阶和六阶紧致差分格式的高精度。
In this paper a family of fourth-order and sixth-order compact difference schemes for the three dimensional (3D) linear Poisson equation are derived in detail. By using finite volume (FV) method for derivation, the highest-order compact schemes based on two different types of dual partitions are obtained. Moreover, a new fourth-order compact scheme is gained and numerical experiments show the new scheme is much better than other known fourth-order schemes. The outline for the nonlinear problems are also given. Numerical experiments are conducted to verify the feasibility of this new method and the high accuracy of these fourth-order and sixth-order compact difference scheme.