LATTICE BOLTZMANN APPROACH TO HIGH-SPEED COMPRESSIBLE FLOWS

X. F. Pan, Aiguo Xu (), Guangcai Zhang and Song Jiang
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X. F. Pan: National Key Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, P. O. Box 8009-26, Beijing 100088, P. R. China
Aiguo Xu: National Key Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, P. O. Box 8009-26, Beijing 100088, P. R. China
Guangcai Zhang: National Key Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, P. O. Box 8009-26, Beijing 100088, P. R. China
Song Jiang: National Key Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, P. O. Box 8009-26, Beijing 100088, P. R. China

International Journal of Modern Physics C (IJMPC), 2007, vol. 18, issue 11, 1747-1764

Abstract: We present an improved lattice Boltzmann model for high-speed compressible flows. The model is composed of a discrete-velocity model by Kataoka and Tsutahara15and an appropriate finite-difference scheme combined with an additional dissipation term. With the dissipation term parameters in the model can be flexibly chosen so that the von Neumann stability condition is satisfied. The influence of the various model parameters on the numerical stability is analyzed and some reference values of parameter are suggested. The new scheme works for both subsonic and supersonic flows with a Mach number up to 30 (or higher), which is validated by well-known benchmark tests. Simulations on Riemann problems with very high ratios (1000:1) of pressure and density also show good accuracy and stability. Successful recovering of regular and double Mach shock reflections shows the potential application of the lattice Boltzmann model to fluid systems where non-equilibrium processes are intrinsic. The new scheme for stability can be easily extended to other lattice Boltzmann models.

Keywords: Lattice Boltzmann; high-speed compressible flow; von Neumann analysis; shock (search for similar items in EconPapers)
Date: 2007
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DOI: 10.1142/S0129183107011716

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