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Modified Monotonicity Preserving Constraints for High-Resolution Optimized Compact Scheme
Journal of Scientific Computing ( IF 2.8 ) Pub Date : 2020-05-06 , DOI: 10.1007/s10915-020-01221-0
Myeong-Hwan Ahn , Duck-Joo Lee

The monotonicity-preserving (MP) scheme is an accurate shock-capturing scheme. However, its performance is still inefficient for resolving high-frequency waves. In this paper, to improve the resolution characteristics, an upwind compact interpolation is proposed as a substitute to the original one in the MP scheme, and the coefficients of that were analytically optimized to minimize the dispersion and dissipation errors. Moreover, it was found that the limiting part of the original MP scheme degenerates the accuracy in a high-wavenumber region due to unnecessarily activation. This limitation is improved by applying a new indicator and criterion. The results of the nonlinear wave (N-wave) propagation demonstrate that the proposed scheme guarantees the robustness at the sharp discontinuity. At the same time, the solutions of linear wave propagation prove the excellent resolution of the proposed scheme. We intensively evaluated the performance for the standard and long-time situations of the shock-entropy wave interaction problems. The results prove that the usefulness of proposed scheme is more pronounced in the flow fields involving both of shock and waves.



中文翻译:

高分辨率优化紧凑方案的修正单调保性约束

保持单调性(MP)方案是一种精确的冲击捕获方案。但是,其性能对于解析高频波仍然无效。在本文中,为了改善分辨率特性,提出了一种迎风紧凑插值法来代替MP方案中的原始插值法,并对其解析系数进行了优化,以最大程度地减小色散和耗散误差。此外,发现原始MP方案的限制部分由于不必要的激活而降低了高波数区域中的精度。通过应用新的指标和标准可以改善此限制。非线性波(N波)传播的结果表明,所提出的方案保证了在急剧不连续处的鲁棒性。同时,线性波传播的解决方案证明了该方案的出色分辨率。我们集中评估了冲击-熵波相互作用问题的标准和长期情况下的性能。结果证明,该方案的实用性在涉及冲击波和冲击波的流场中更为明显。

更新日期:2020-05-06
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