On the use of Mühlbach expansions in the recovery step of ENO methods
On the use of Mühlbach expansions in the recovery step of ENO methods
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DOI：
10.1007/s002110050252
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发表时间：
1997-03
影响因子：
2.1
通讯作者：
R. Abgrall;T. Sonar
中科院分区：
文献类型：
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作者：
R. Abgrall;T. Sonar
在可压缩流体流动的数值模拟中，在三角形网格上的现代基本无振荡（ENO）激波捕获方法中，恢复步骤是最昂贵的算法成分。虽然牛顿形式的恢复多项式被用于一维ENO格式，但这种有用且数值稳定的多项式形式是否存在于多维中尚不清楚。正如在[1]中所观察到的，Mühlbach在随后的两篇论文[15]和[16]中对这个问题提供了一个非常一般的答案。我们概括了他的插值理论进一步恢复一般的问题，并概述了使用Mühlbach的扩展ENO计划。数值例子表明，这种方法的有用性的问题中恢复从细胞平均数据。
The recovery step is the most expensive algorithmic ingredient in modern essentially non-oscillatory (ENO) shock capturing methods on triangular meshes for the numerical simulation of compressible fluid flow. While recovery polynomials in Newton form are used in one-dimensional ENO schemes it isa priorinot clear whether such useful as well as numerically stable form of polynomials exists in multiple dimensions. As was observed in [1] a very general answer to this question was provided by Mühlbach in two subsequent papers [15] and [16]. We generalise his interpolation theory further to the general recovery problem and outline the use of Mühlbach's expansion in ENO schemes. Numerical examples show the usefulness of this approach in the problem of recovery from cell average data.