Application of the space-time conservation element and solution element method to one-dimensional convection-diffusion problems
Application of the space-time conservation element and solution element method to one-dimensional convection-diffusion problems
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DOI：
10.1006/jcph.2000.6610
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发表时间：
2000-11
影响因子：
4.1
通讯作者：
Sin-Chung Chang;Xiao-Yen J. Wang;Wai Ming To
中科院分区：
文献类型：
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作者：
Sin-Chung Chang;Xiao-Yen J. Wang;Wai Ming To
在时空守恒元与解元（CE/SE）方法中，所使用的独立推进变量不仅包括物理因变量的网格值，而且与典型数值方法不同，还包括这些物理变量的空间导数的网格值。使用额外的行进变量是因为需要构建两级，显式和非耗散方案，这是CE/SE开发的核心。这也是由于需要尽量减少模板，同时保持精度。本文以1D a -μ方案为例，评估了这种增加的复杂性对一致性、准确性和运算次数的影响。作为这项工作的一部分，引入了一种等效但更有效的a -μ格式，其中独立的行进变量是绑定到每个网格点的局部通量。此外，a -μ之间存在着有趣的关系。进一步探讨了Leapfrog和DuFort-Frankel方案。此外，还讨论了Leapfrog方案、DuFort-Frankel方案和Lax方案的冗余及其补救措施。最后给出了无粘Burgers方程的CE/SE求解器的构造和评价。
Abstract In the space–time conservation element and solution element (CE/SE) method, the independent marching variables used comprise not only the mesh values of the physical dependent variables but also, in contrast to a typical numerical method, the mesh values of the spatial derivatives of these physical variables. The use of the extra marching variables results from the need to construct the two-level, explicit and nondissipative schemes which are at the core of the CE/SE development. It also results from the need to minimize the stencil while maintaining accuracy. In this paper, using the 1D a –μ scheme as an example, the effect of this added complication on consistency, accuracy, and operation count is assessed. As part of this effort, an equivalent yet more efficient form of the a –μ scheme in which the independent marching variables are the local fluxes tied to each mesh point is introduced. Also, the intriguing relations that exist among the a –μ. Leapfrog, and DuFort–Frankel schemes are further explored. In addition, the redundancy of the Leapfrog, DuFort–Frankel, and Lax schemes and the remedy for this redundancy are discussed. This paper is concluded with the construction and evaluation of a CE/SE solver for the inviscid Burgers equation.