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

Part of: Permutation groups

Published online by Cambridge University Press:  08 July 2016

Yu Sun ,
Chang Shu ,
Liming Yang  and
C. J. Teo
Yu Sun
Affiliation:
Department of Mechanical Engineering, National University of Singapore 10 Kent Ridge Crescent , Singapore 119260, Singapore
Chang Shu*
Affiliation:
Department of Mechanical Engineering, National University of Singapore 10 Kent Ridge Crescent , Singapore 119260, Singapore
Liming Yang
Affiliation:
Department of Aerodynamics, College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, Yudao Street, Nanjing 210016, China
C. J. Teo
Affiliation:
Department of Mechanical Engineering, National University of Singapore 10 Kent Ridge Crescent , Singapore 119260, Singapore
*
*Corresponding author. Email:mpeshuc@nus.edu.sg (C. Shu)
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Abstract

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.

Keywords

Switch functiongas-kinetic schemenumerical dissipationinviscid and viscous flows

MSC classification

Secondary: 20B40: Computational methods
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 8 , Issue 5 , October 2016 , pp. 703 - 721
Copyright
Copyright © Global-Science Press 2016 

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