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A Switch Function-Based Gas-Kinetic Scheme for Simulation of Inviscid and Viscous Compressible Flows

Published online by Cambridge University Press:  08 July 2016

Yu Sun
Department of Mechanical Engineering, National University of Singapore 10 Kent Ridge Crescent , Singapore 119260, Singapore
Chang Shu*
Department of Mechanical Engineering, National University of Singapore 10 Kent Ridge Crescent , Singapore 119260, Singapore
Liming Yang
Department of Aerodynamics, College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, Yudao Street, Nanjing 210016, China
C. J. Teo
Department of Mechanical Engineering, National University of Singapore 10 Kent Ridge Crescent , Singapore 119260, Singapore
*Corresponding author. (C. Shu)
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In this paper, a switch function-based gas-kinetic scheme (SF-GKS) is presented for the simulation of inviscid and viscous compressible flows. With the finite volume discretization, Euler and Navier-Stokes equations are solved and the SF-GKS is applied to evaluate the inviscid flux at cell interface. The viscous flux is obtained by the conventional smooth function approximation. Unlike the traditional gas-kinetic scheme in the calculation of inviscid flux such as Kinetic Flux Vector Splitting (KFVS), the numerical dissipation is controlled with a switch function in the present scheme. That is, the numerical dissipation is only introduced in the region around strong shock waves. As a consequence, the present SF-GKS can well capture strong shock waves and thin boundary layers simultaneously. The present SF-GKS is firstly validated by its application to the inviscid flow problems, including 1-D Euler shock tube, regular shock reflection and double Mach reflection. Then, SF-GKS is extended to solve viscous transonic and hypersonic flow problems. Good agreement between the present results and those in the literature verifies the accuracy and robustness of SF-GKS.

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Research Article
Copyright © Global-Science Press 2016 

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