Monotonicity preserving weighted essentially non-oscillatory schemes with increasingly high order of accuracy
Monotonicity preserving weighted essentially non-oscillatory schemes with increasingly high order of accuracy
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DOI：
10.1006/jcph.2000.6443
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发表时间：
2000-05-20
影响因子：
4.1
通讯作者：
Shu, CW
中科院分区：
文献类型：
--
作者：
Balsara, DS;Shu, CW
在本文中，我们设计了一类数值格式，它们是G. - S. Jiang和C. - W，Shu（1996）和X. - D. Liu，S. Osher，和T. Chan（1994），单独使用时，这些格式不一定是单调保持的，但与A的单调保持界相耦合。Suresh和H. t. Huynh（1997）的方法，得到的保持单调性的加权基本无振荡（MPWENO）格式具有高的相位精度和高阶精度。该族的高阶成员对于光滑问题几乎是谱精确的，然而，它们具有鲁棒的激波捕获能力。该格式在正常CFL数下是稳定的。它们也是高效的，并且不具有比该同一系列方案的低阶成员大得多的计算复杂度。更高的精度，这些计划提供加上其相对较低的计算复杂性，使他们可行的竞争对手，低阶计划，如旧的总变差递减计划，包含不连续性和丰富的光滑区域结构的问题。我们描述的MPWENO计划在这里，以及显示他们的能力，以达到他们的设计精度，流畅。我们还研究了陡化算法的作用，如人工压缩方法在设计非常高阶的计划。在一个和两个维度的几个测试问题。对于多维问题的流动是不对齐的任何网格方向，它示出了本计划有一个很大的优势，较低的顺序计划。作者认为，本文设计的方法对于可压缩湍流的直接数值模拟和大涡模拟具有很大的实用性。该方法也适用于其他双曲方程组，并证明了MPWENO格式在磁流体力学试验问题上也能很好地工作。(C)北京大学出版社.
In this paper we design a class of numerical schemes that are higher-order extensions of the weighted essentially non-oscillatory (WENO) schemes of G.-S. Jiang and C.-W, Shu (1996) and X.-D. Liu, S. Osher, and T. Chan (1994), Used by themselves, the schemes may not always be monotonicity preserving but coupled with the monotonicity preserving bounds of A. Suresh and H. T. Huynh (1997) they perform very well, The resulting monotonicity preserving weighted essentially non-oscillatory (MPWENO) schemes have high phase accuracy and high order of accuracy. The higher-order members of this family are almost spectrally accurate for smooth problems, Nevertheless, they, have robust shock capturing ability. The schemes are stable under normal CFL numbers. They are also efficient and do not have a computational complexity that is substantially greater than that of the lower-order members of this same family of schemes. The higher accuracy that these schemes offer coupled with their relatively low computational complexity makes them viable competitors to lower-order schemes, such as the older total variation diminishing schemes, for problems containing both discontinuities and rich smooth region structure. We describe the MPWENO schemes here as well as show their ability to reach their designed accuracies for smooth flow. We also examine the role of steepening algorithms such as the artificial compression method in the design of very high order schemes. Several test problems in one and two dimensions are presented. For multidimensional problems where the flow is not aligned with any of the grid directions it is shown that the present schemes have a substantial advantage over lower-order schemes. It is argued that the methods designed here have great utility for direct numerical simulations and large eddy simulations of compressible turbulence. The methodology developed hen is applicable to other hyperbolic systems, which is demonstrated by showing that the MPWENO schemes also work very well on magnetohydrodynamical test problems. (C) 2000 Academic Press.