A robust low‐dissipation AUSM‐family scheme for numerical shock stability on unstructured grids |
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| Authors: | Fan Zhang Jun Liu Biaosong Chen Wanxie Zhong |
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| Affiliation: | 1. Department of Engineering Mechanics, Dalian University of Technology, Dalian, China;2. State Key Laboratory of Structure Analysis for Industrial Equipment, Dalian University of Technology, Dalian, China;3. School of Aeronautics and Astronautics, Dalian University of Technology, Dalian, China |
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| Abstract: | The simple low‐dissipation advection upwind splitting method (SLAU) scheme is a parameter‐free, low‐dissipation upwind scheme that has been applied in a wide range of aerodynamic numerical simulations. In spite of its successful applications, the SLAU scheme could be showing shock instabilities on unstructured grids, as many other contact resolved upwind schemes. Therefore, a hybrid upwind flux scheme is devised for improving the shock stability of SLAU scheme, without compromising on accuracy and low Mach number performance. Numerical flux function of the hybrid scheme is written in a general form, in which only the scalar dissipation term is different from that of the SLAU scheme. The hybrid dissipation term is defined by using a differentiable multidimensional‐shock‐detection pressure weight function, and the dissipation term of SLAU scheme is combined with that of the Van Leer scheme. Furthermore, the hybrid dissipation term is only applied for the solution of momentum fluxes in numerical flux function. Based on the numerical test results, the hybrid scheme is deemed to be a successful improvement on the shock stability of SLAU scheme, without compromising on the efficiency and accuracy. Copyright © 2016 John Wiley & Sons, Ltd. |
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| Keywords: | SLAU scheme shock instabilities unstructured grids hybrid scheme scalar dissipation term momentum fluxes |
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