A family of high-order targeted ENO schemes for compressible-fluid simulations
A family of high-order targeted ENO schemes for compressible-fluid simulations
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DOI：
10.1016/j.jcp.2015.10.037
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发表时间：
2016-01
期刊：
影响因子：
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通讯作者：
Lin Fu;Xiangyu Y. Hu;N. Adams
中科院分区：
文献类型：
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作者：
Lin Fu;Xiangyu Y. Hu;N. Adams
虽然经典的韦诺方案取得了巨大的成功，并被广泛接受，他们表现出一些缺点。它们对于湍流的直接模拟来说太耗散，并且当非常高阶的版本应用于复杂流动时缺乏鲁棒性。在本文中，我们提出了一个家庭的高阶目标ENO格式，适用于可压缩流体模拟涉及广泛的流动尺度。为了提高数值鲁棒性相比，非常高阶的经典韦诺计划，重建动态组装一组低阶候选stentums递增的宽度。虽然不连续性和小规模的波动被有效地分离，数值耗散显着减少了一个ENO样的模板选择，它要么应用一个候选模板与其原始的线性权重，或删除它的贡献时，它是交叉的不连续性。背景线性格式在保持近似色散-耗散关系的约束下进行优化。通过拟线性分析和实际数值试验，确定了一组与情况无关的参数。任意高阶格式的一般公式是以一种简单的方式。各种基准测试问题，包括宽带波，强冲击和接触不连续性进行了研究。与经典的韦诺格式相比，该格式具有较好的鲁棒性、较低的数值耗散和较强的间断捕捉能力。它们特别适用于激波-湍流相互作用的DNS和LES。
Although classical WENO schemes have achieved great success and are widely accepted, they exhibit several shortcomings. They are too dissipative for direct simulations of turbulence and lack robustness when very-high-order versions are applied to complex flows. In this paper, we propose a family of high-order targeted ENO schemes which are applicable for compressible-fluid simulations involving a wide range of flow scales. In order to increase the numerical robustness as compared to very-high-order classical WENO schemes, the reconstruction dynamically assembles a set of low-order candidate stencils with incrementally increasing width. While discontinuities and small-scale fluctuations are efficiently separated, the numerical dissipation is significantly diminished by an ENO-like stencil selection, which either applies a candidate stencil with its original linear weight, or removes its contribution when it is crossed by a discontinuity. The background linear scheme is optimized under the constraint of preserving an approximate dispersion–dissipation relation. By means of quasi-linear analyses and practical numerical experiments, a set of case-independent parameters is determined. The general formulation of arbitrarily high-order schemes is presented in a straightforward way. A variety of benchmark-test problems, including broadband waves, strong shock and contact discontinuities are studied. Compared to well-established classical WENO schemes, the present schemes exhibit significantly improved robustness, low numerical dissipation and sharp discontinuity capturing. They are particularly suitable for DNS and LES of shock–turbulence interactions.