On the improvement of the all-speed flux scheme for very low Mach number flows
On the improvement of the all-speed flux scheme for very low Mach number flows
复制标题
极低马赫数流全速通量方案的改进
DOI：
10.2514/6.2013-2696
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发表时间：
2013
期刊：
影响因子：
--
通讯作者：
E. Shima
中科院分区：
文献类型：
--
作者：
E. Shima
本文讨论了可压缩流动的计算流体动力学中计算流体动力学方法的关键要素——无粘数值通量函数。在可压缩CFD方法MUSCL（Monotone up风为中心的守恒律方案）中，采用平流上游分裂法（Advection Upstream Splitting Method， AUSM）型全速度数值通量格式，如slu （Simple Low耗散AUSM）或SD-SLAU(Shock detection SLAU)，可以同时求解低马赫数流动和声音传播，而不损失精度，也不需要调整参数。然而，据报道，它们有时会在非常低马赫数（M<0.01）的流动中产生摆动。本文提出了一种新的数值通量格式，称为WS (Wiggle-Sensing) SLAU，旨在减少摆动，同时保持SLAU的其他有利特性，如计算声音传播的能力。通过一维声传播、极弱激波管和翼型绕流的数值算例验证了该方案的有效性。
This article deals with inviscid numerical flux functions, those are key elements in the CFD(Computational Fluid Dynamics) methods, for the computational fluid dynamics for compressible flows. By using AUSM(Advection Upstream Splitting Method) type all-speed numerical flux schemes, such as SLAU(Simple Low Dissipative AUSM) or SD-SLAU(Shock Detecting SLAU), in MUSCL(Monotone Upwind-centered Scheme for Conservation Law) approach for compressible CFD, low Mach number flows and sound propagations can be solved at the same time without loss of accuracy nor parameter adjustment. However, it has been reported that, they sometimes produce the wiggle at very low Mach number (M<0.01) flows. The new numerical flux scheme, named WS (Wiggle-Sensing) SLAU is formulated in this paper, aiming to diminish wiggles with keeping other favorable feature of SLAU, such as capability to compute sound propagation. The effectiveness of the new scheme is shown by numerical examples, including one dimensional sound propagation, very weak shock tube and flow around an airfoil.