混合低扩散近似黎曼求解器用于雷诺应力输运方程
Hybrid low-diffusion approximate Riemann solvers for Reynolds-stress transport
AI总结：
本文提出混合低扩散近似黎曼求解器用于雷诺应力输运方程，通过分析不同等效形式的RSM-RANS系统，揭示了湍流闭合复杂项的分类，并通过计算示例展示了该方法在处理雷诺应力时的非物理振荡问题。
摘要：
本文研究了低扩散（接触间断分辨）近似黎曼求解器在雷诺平均纳维-斯托克斯（RANS）方程的卷积部分中用于雷诺应力模型（RSM）闭合的应用。讨论了不同等效形式的RSM-RANS系统，并尝试对高级湍流闭合引入的复杂项进行分类。展示了计算示例，表明使用能分辨接触间断的卷积数值通量以及被动标量方法来处理雷诺应力可能引起非物理振荡。为确定这些不稳定性来源，对简化雷诺应力输运模型系统的黎曼问题进行了理论分析，该模型在平均流方程的卷积部分中包含雷诺应力张量的散度，并只包含那些可计算的非守恒乘积。提出了混合解法，允许将任何低扩散近似黎曼求解器与高级模型中使用的复杂张量表示结合，结合低扩散的均流方程通量与更耗散的雷诺应力输运质量通量。展示了多个计算示例以评估该方法的性能。
英文摘要：
The paper investigates the use of low-diffusion (contact-discontinuity-resolving [Liou M.S.: {\em J. Comp. Phys.} {\bf 160} (2000) 623--648]) approximate Riemann solvers for the convective part of the Reynolds-averaged Navier-Stokes (\tsn{RANS}) equations with Reynolds-stress model (\tsn{RSM}) closure. Different equivalent forms of the \tsn{RSM-RANS} system are discussed and classification of the complex terms introduced by advanced turbulence closures is attempted. Computational examples are presented, which indicate that the use of contact-discontinuity-resolving convective numerical fluxes, along with a passive-scalar approach for the Reynolds-stresses, may lead to unphysical oscillations of the solution. To determine the source of these instabilities, theoretical analysis of the Riemann problem for a simplified Reynolds-stress transport model-system, which incorporates the divergence of the Reynolds-stress tensor in the convective part of the mean-flow equations, and includes only those nonconservative products which are computable (do not require modelling), was undertaken, highlighting the differences in wave-structure compared to the passive-scalar case. A hybrid solution, allowing the combination of any low-diffusion approximate Riemann solver with the complex tensorial representations used in advanced models, is proposed, combining low-diffusion fluxes for the mean-flow equations with a more dissipative massflux for Reynolds-stress-transport. Several computational examples are presented to assess the performance of this approach.
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