Article: Modified gas-kinetic scheme for shock structures in argon Journal: Progress in Computational Fluid Dynamics, An International Journal (PCFD) 2008 Vol.8 No.1/2/3/4 pp.97 - 108 Abstract: The gas-kinetic scheme (GKS) is a finite-volume method in which the fluxes are constructed from the single particle velocity distribution function f. The distribution function f is obtained from the linearised Boltzmann equation and is retained only to the Navier-Stokes order in terms of the Chapman-Enskog expansion. Higher order non-equilibrium effects are included in a variable local particle collision time depending on local gradients of the hydrodynamic variables up to second order. The fluxes so constructed possess the non-equilibrium information beyond the linear constitutive relations and Fourier law. The modified gas-kinetic scheme with a local particle collision time λ* depending on the gradients of hydrodynamic variables is used to compute shock structures in argon for Mach numbers between 1.2 and 25.0. We validate our results with existing numerical and experimental ones. Our results show that the modified gas-kinetic scheme is effective and efficient for shock structure calculations. Inderscience Publishers - linking academia, business and industry through research

Title: Modified gas-kinetic scheme for shock structures in argon

Authors: Wei Liao, Yan Peng, Li-Shi Luo, Kun Xu

Addresses: Department of Mathematics and Statistics and Center for Computational Sciences, Old Dominion University, Norfolk, Virginia 23529, USA. ' Department of Mathematics and Statistics and Center for Computational Sciences, Old Dominion University, Norfolk, Virginia 23529, USA. ' Department of Mathematics and Statistics and Center for Computational Sciences, Old Dominion University, Norfolk, Virginia 23529, USA. ' Department of Mathematics, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong

Abstract: The gas-kinetic scheme (GKS) is a finite-volume method in which the fluxes are constructed from the single particle velocity distribution function f. The distribution function f is obtained from the linearised Boltzmann equation and is retained only to the Navier-Stokes order in terms of the Chapman-Enskog expansion. Higher order non-equilibrium effects are included in a variable local particle collision time depending on local gradients of the hydrodynamic variables up to second order. The fluxes so constructed possess the non-equilibrium information beyond the linear constitutive relations and Fourier law. The modified gas-kinetic scheme with a local particle collision time λ* depending on the gradients of hydrodynamic variables is used to compute shock structures in argon for Mach numbers between 1.2 and 25.0. We validate our results with existing numerical and experimental ones. Our results show that the modified gas-kinetic scheme is effective and efficient for shock structure calculations.

Keywords: collision time; gas kinetic scheme; GKS; non-equilibrium ﬂow; shock structures; argon; finite volume method; Boltzmann equation.

DOI: 10.1504/PCFD.2008.018082

Progress in Computational Fluid Dynamics, An International Journal, 2008 Vol.8 No.1/2/3/4, pp.97 - 108

Published online: 30 Apr 2008 *

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Title: Modified gas-kinetic scheme for shock structures in argon

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