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首页> 外文期刊>Journal of Computational Physics >Development of nonlinear weighted compact schemes with increasingly higher order accuracy
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Development of nonlinear weighted compact schemes with increasingly higher order accuracy

机译：开发非线性加权紧凑型方案，顺序越来越高的精度

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In this paper, we design a class of high order accurate nonlinear weighted compact schemes that are higher order extensions of the nonlinear weighted compact schemes proposed by Deng and Zhang [X. Deng, H. Zhang, Developing high-order weighted compact nonlinear schemes, J. Comput. Phys. 165 (2000) 22-44] and the weighted essentially non-oscillatory schemes of Jiang and Shu [G.-S. Jiang, C.-W. Shu, Efficient implementation of weighted ENO schemes, J. Comput. Phys. 126 (1996) 202-228] and Balsara and Shu [D.S. Balsara, C.-W. Shu, Monotonicity preserving weighted essentially non-oscillatory schemes with increasingly high order of accuracy, J. Comput. Phys. 160 (2000) 405-452]. These nonlinear weighted compact schemes are proposed based on the cell-centered compact scheme of Lele [S.K. Lele, Compact finite difference schemes with spectral-like resolution, J. Comput. Phys. 103 (1992) 16-42]. Instead of performing the nonlinear interpolation on the conservative variables as in Deng and Zhang (2000), we propose to directly interpolate the flux on its stencil. Using the Lax-Friedrichs flux splitting and characteristic-wise projection, the resulted interpolation formulae are similar to those of the regular WENO schemes. Hence, the detailed analysis and even many pieces of the code can be directly copied from those of the regular WENO schemes. Through systematic test and comparison with the regular WENO schemes, we observe that the nonlinear weighted compact schemes have the same ability to capture strong discontinuities, while the resolution of short waves is improved and numerical dissipation is reduced. (c) 2008 Elsevier Inc. All rights reserved.
机译：在本文中，我们设计了一类高阶精确的非线性加权紧凑型紧凑型，是DENG和ZHANG [X.邓，H.张，开发高阶加权紧凑型非线性方案，J.Copp。物理。 165（2000）22-44]和江和舒的重量基本上非振荡方案[G.0.江，C. -w。 SHU，高效实施加权eno方案，J.Copp。物理。 126（1996）202-228]和Balsara和Shu [D.S. Balsara，C. -w。 SHU，单调性保存加权基本上非振荡方案，具有越来越高的准确度，J.Copl。物理。 160（2000）405-452]。这些非线性加权紧凑型方案是基于leel的细胞中心紧凑方案的[S.K. LELE，具有光谱样谱的紧凑型有限差分方案，J.Copl。物理。 103（1992）16-42]。在邓和张（2000）中，我们建议直接在其模板上立即将通量直接插入保守变量上的非线性插值。使用LAX-Friedrichs助焊剂分裂和特性 - 明智的投影，所得到的插值公式类似于常规Weno方案的内插公式。因此，可以直接从常规Weno方案的那些直接复制详细分析甚至许多代码。通过系统测试和与常规Weno方案进行比较，观察到非线性加权紧凑型方案具有相同的捕获强不连续性的能力，而短波的分辨率得到改善，并且减少了数值耗散。 （c）2008年elestvier Inc.保留所有权利。

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