Journal
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
Volume 387, Issue 8-9, Pages 1721-1732Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.physa.2007.11.013
Keywords
lattice boltzmann method; compressible flows; von neumann analysis
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In this paper we present an improved lattice Boltzmann model for compressible Navier-Stokes system with high Mach number. The model is composed of three components: (i) the discrete-velocity-model by M. Watari and M. Tsutahara [Phys. Rev. E 67 (2003) 036306], (ii) a modified Lax-Wendroff finite difference scheme where reasonable dissipation and dispersion are naturally included, (iii) artificial viscosity. The improved model is convenient to compromise the high accuracy and stability. The included dispersion term can effectively reduce the numerical oscillation at discontinuity. The added artificial viscosity helps the scheme to satisfy the von Neumann stability condition. Shock tubes and shock reflections are used to validate the new scheme. In our numerical tests the Mach numbers are successfully increased up to 20 or higher. The flexibility of the new model makes it suitable for tracking shock waves with high accuracy and for investigating nonlinear nonequilibrium complex systems. (c) 2007 Elsevier B.V. All fights reserved.
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