A New Approach for Constructing Highly Stable High Order Cese Schemes
A New Approach for Constructing Highly Stable High Order Cese Schemes
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DOI：
10.2514/6.2010-543
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发表时间：
2013-07
期刊：
影响因子：
--
通讯作者：
Sin-Chung Chang
中科院分区：
文献类型：
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作者：
Sin-Chung Chang
提出了一种构造高阶CESE格式的新方法，该方法避免了传统高阶格式的共同缺点，包括：（a）对计算不稳定性的敏感性;（B）由于其局部隐式性质（即，在每个网格点处，需要求解涉及与该网格点相关联的所有网格变量的线性/非线性方程系统）;（c）使用大的和复杂的扩展，这使得边界处理复杂化，并且还使得有效的并行计算更加困难;（d）在涉及复杂几何形状的应用中的困难;和（e）使用解决稳定性问题所需的特定问题技术，但这些技术往往会引起不希望的副作用。事实上，它将被证明，在概念上的飞跃的帮助下，人们可以从一个给定的二阶CESE计划建立其第四，第六，第八，.的版本，具有相同的模板和相同的稳定性条件的二阶计划，也保留了所有其他的优点，后者的计划。还将提供多维扩展的草图。
A new approach is devised to construct high order CESE schemes which would avoid the common shortcomings of traditional high order schemes including: (a) susceptibility to computational instabilities; (b) computational inefficiency due to their local implicit nature (i.e., at each mesh points, need to solve a system of linear/nonlinear equations involving all the mesh variables associated with this mesh point); (c) use of large and elaborate stencils which complicates boundary treatments and also makes efficient parallel computing much harder; (d) difficulties in applications involving complex geometries; and (e) use of problem-specific techniques which are needed to overcome stability problems but often cause undesirable side effects. In fact it will be shown that, with the aid of a conceptual leap, one can build from a given 2nd-order CESE scheme its 4th-, 6th-, 8th-,... order versions which have the same stencil and same stability conditions of the 2nd-order scheme, and also retain all other advantages of the latter scheme. A sketch of multidimensional extensions will also be provided.