A COMPACT UPWIND SECOND ORDER SCHEME FOR THE EIKONAL EQUATION
A COMPACT UPWIND SECOND ORDER SCHEME FOR THE EIKONAL EQUATION
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Ekonal方程的紧凑迎风二阶方案
DOI：
10.4208/jcm.1003-m0014
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发表时间：
2010
影响因子：
0.9
通讯作者：
Zhao
中科院分区：
文献类型：
--
作者：
Benamou;Songting;Luo;Hongkai;Zhao
本文提出了一个计算Eikonal方程粘性解的二阶紧致迎风格式，它是基于：1.数值观察表明，经典的一阶单调迎风格式产生的数值迎风梯度在奇点处也是一阶精度; 2.关于解的二阶导数的部分信息是已知的，并且在Eikonal方程的结构中给出，并且可以用于减小模板的尺寸。我们实现了二阶格式作为对众所周知的扫描方法的修正，但它应该适用于任何一阶单调迎风格式，需要注意选择适当的展度以避免不稳定性，并给出了数值例子。
We present a compact upwind second order scheme for computing the viscosity solution of the Eikonal equation.This new scheme is based on: 1.the numerical observation that classical first order monotone upwind schemes for the Eikonal equation yield numerical upwind gradient which is also first order accurate up to singularities; 2.a remark that partial information on the second derivatives of the solution is known and given in the structure of the Eikonal equation and can be used to reduce the size of the stencil. We implement the second order scheme as a correction to the well known sweeping method but it should be applicable to any first order monotone upwind scheme.Care is needed to choose the appropriate stencils to avoid instabilities.Numerical examples are presented.