A stable hybrid Roe scheme on triangular grids,International Journal for Numerical Methods in Fluids

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A stable hybrid Roe scheme on triangular grids
International Journal for Numerical Methods in Fluids ( IF 1.7 ) Pub Date : 2020-09-28 , DOI: 10.1002/fld.4916
Sutthisak Phongthanapanich ₁

Affiliation

Numerical shock instability is a common problem for shock‐capturing methods that try to resolve contact and shear waves with minimal diffusion. Most flux‐difference splitting and the AUSM family of schemes produce the carbuncle phenomenon on both structured and unstructured grids. The original Roe scheme is well known to generate shock anomalies and can lead to nonentropic weak solutions to the Euler equations. A simple and robust approach for healing these numerical instabilities is to apply the hybrid technique incorporated with an efficient weighting switch function to control the amount of dissipation in the vicinity of shock waves. This article proposes a simple, robust, and accurate hybrid Roe scheme (Roe+ scheme) by hybridizing the Roe scheme and the modified AUSMV+ scheme. A new normalized pressure/density‐based weighting switch function is proposed and applied to the scheme to minimize the numerical dissipation and maintain the robustness of the hybridization. The linearized discrete analysis is performed to evaluate the proposed scheme according to the perturbation damping mechanism of an odd–even decoupling problem. The resulting recursive equations indicate that the hybridized mechanism damps all perturbations effectively. Finally, several numerical examples demonstrated that the Roe+ scheme provides an accurate, robust, and carbuncle‐free solution on both structured and unstructured triangular grids.

中文翻译：

三角形网格上的稳定混合 Roe 方案

数值冲击不稳定性是冲击捕获方法的一个常见问题，这些方法试图以最小的扩散来解决接触波和剪切波。大多数通量差分裂和 AUSM 系列方案都会在结构化和非结构化网格上产生痈现象。众所周知，原始 Roe 方案会产生冲击异常，并可能导致欧拉方程的非熵弱解。治愈这些数值不稳定性的一种简单而可靠的方法是应用混合技术，结合有效的加权开关功能来控制冲击波附近的耗散量。本文通过将 Roe 方案和修改后的 AUSMV+ 方案进行混合，提出了一种简单、稳健、准确的混合 Roe 方案（Roe+ 方案）。提出了一种新的基于归一化压力/密度的加权切换函数，并将其应用于该方案以最小化数值耗散并保持杂交的鲁棒性。根据奇偶解耦问题的微扰阻尼机制，执行线性化离散分析以评估所提出的方案。得到的递归方程表明混合机制有效地抑制了所有扰动。最后，几个数值例子表明 Roe+ 方案在结构化和非结构化三角形网格上都提供了准确、稳健且无痈的解决方案。根据奇偶解耦问题的扰动阻尼机制，执行线性化离散分析以评估所提出的方案。得到的递归方程表明混合机制有效地抑制了所有扰动。最后，几个数值例子表明 Roe+ 方案在结构化和非结构化三角形网格上都提供了准确、稳健且无痈的解决方案。根据奇偶解耦问题的扰动阻尼机制，执行线性化离散分析以评估所提出的方案。得到的递归方程表明混合机制有效地抑制了所有扰动。最后，几个数值例子表明 Roe+ 方案在结构化和非结构化三角形网格上都提供了准确、稳健且无痈的解决方案。

更新日期：2020-09-28

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