A new formulation for two-wave Riemann solver accurate at contact interfaces
A new formulation for two-wave Riemann solver accurate at contact interfaces
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DOI：
10.1063/1.5083888
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发表时间：
2019-04-01
影响因子：
4.6
通讯作者：
Xiao, Feng
中科院分区：
文献类型：
--
作者：
Deng, Xi;Boivin, Pierre;Xiao, Feng
这项研究提出了 Harten、Lax 和 van Leer (HLL) 型黎曼求解器的新公式，它能够准确地求解接触不连续性，但对强冲击具有鲁棒性。众所周知，原始 HLL 具有不完整的波结构，耗散太大，无法准确捕获接触不连续性。另一方面，接触捕获近似黎曼求解器，例如带有接触的 HLL (HLLC)，通常会受到强冲击的杂散解，也称为碳化现象。在这项工作中，通过用 BVD 算法修改原始 HLL，提出了一种新的精确且鲁棒的 HLL 类型公式，即所谓的 HLL-BVD（边界变化递减的 HLL 黎曼求解器）。所提出的方法不是像 HLLC 那样显式地恢复完整的波结构，而是通过类似跳跃的函数来恢复丢失的接触。通过最小化 HLL 中的固有耗散项，可以进一步提高解决接触不连续性的能力。在不修改HLL原有不完整波浪结构的情况下，保留了对强冲击的鲁棒性。因此，所提出的方法不存在冲击不稳定问题。通过解决几个一维和二维测试证明了新方法的准确性和鲁棒性。结果表明，基于两波 HLL 型黎曼求解器的新公式不仅能够比原始 HLL 或 HLLC 更准确地捕获接触波，而且最重要的是，对于强冲击具有自由形式的痈不稳定性。由 AIP Publishing 许可发布。
This study proposes a new formulation for the Harten, Lax, and van Leer (HLL) type Riemann solver which is capable of solving contact discontinuities accurately but with robustness for strong shock. It is well known that the original HLL, which has incomplete wave structures, is too dissipative to capture contact discontinuities accurately. On the other side, contact capturing approximate Riemann solvers such as HLL with Contact (HLLC) usually suffer from spurious solutions, also called carbuncle phenomenon, for strong shock In this work, a new accurate and robust HLL type formulation, the so-called HLL-BVD (HLL Riemann solver with boundary variation diminishing) is proposed by modifying the original HLL with the BVD algorithm. Instead of explicitly recovering the complete wave structures like the way of HLLC, the proposed method restores the missing contact with a jump-like function. The capability of solving contact discontinuities is further improved by minimizing the inherent dissipation term in HLL. Without modifying the original incomplete wave structures of HLL, the robustness for strong shock has been reserved. Thus, the proposed method is free from the shock instability problem. The accuracy and robustness of the new method are demonstrated through solving several one- and two-dimensional tests. Results indicate that the new formulation based on the two-wave HLL-type Riemann solver is not only capable of capturing contact waves more accurately than the original HLL or HLLC but, most importantly, is free form carbuncle instability for strong shock. Published under license by AIP Publishing.