Improving Solution of Euler Equations by a Gas-Kinetic BGK Method

Liu Ya; Gao Chao; F. Liu

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Improving Solution of Euler Equations by a Gas-Kinetic BGK Method

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Aim. The well known JST(Jameson-Schmidt-Turkel) scheme requires the use of a dissipation term. We propose using gas-kinetic BGK (Bhatnagar-Gross-Krook) method, which is based on the more fundamental Boltzmann equation, in order to obviate the use of dissipation term and obtain, we believe, an improved solution. Section 1 deals essentially with three things: (1) as analytical solution of molecular probability density function at the ceil interface has been obtained by the Bohzmann equation with BGK model, we can compute the flux term by integrating the density function in the phase space; eqs. (8) and (11) require careful attention; (2) the integrations can be expressed as the moments of Maxwellian distribution with different limits according to the analytical solution; eqs. (9) and (10) require careful attention; (3) the discrete equation by finite volume method can be solved using the time marching method. Computations are performed by the BGK method for the Sod's shock tube problem and a two-dimensional shock reflection problem. The results are compared with those of the conventional JST scheme in Figs. 1 and 2. The BGK method provides better resolution of shock waves and other features of the flow fields.

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《西北工业大学学报》 |2009年第1期|1-5|共5页
作者
Liu Ya; Gao Chao; F. Liu;
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National Key Laboratory of Aerodynamic Design and Research, Northwestern Polytechnical University, Xi'an 710072, China;

National Key Laboratory of Aerodynamic Design and Research, Northwestern Polytechnical University, Xi'an 710072, China;

Department of Mechanical and Aerospace Engineering, University of California, Irvine, CA 92697-3975, USA;

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Improving Solution of Euler Equations by a Gas-Kinetic BGK Method

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