2010/10/31 by Yanbiao Gan, Aiguo Xu, Guangcai Zhang +1 · 2 citations
Physics and Astronomy · #cond-mat.soft #nlin.CG #physics.comp-ph #physics.plasm-ph
paper · pdf · doi:10.1103/physreve.83.056704
published as Physical Review E 83, 056704 (2011) · Accepted for publication in PRE
arxiv created 2011/03/31 · arxiv updated 2015/05/20
A two-dimensional lattice Boltzmann model with 19 discrete velocities for compressible Euler equations is proposed (D2V19-LBM). The fifth-order Weighted Essentially Non-Oscillatory (5th-WENO) finite difference scheme is employed to calculate the convection term of the lattice Boltzmann equation. The validity of the model is verified by comparing simulation results of the Sod shock tube with its corresponding analytical solutions. The velocity and density gradient effects on the Kelvin-Helmholtz instability (KHI) are investigated using the proposed model. Sharp density contours are obtained in our simulations. It is found that, the linear growth rate γ for the KHI decreases with increasing the width of velocity transition layer Dv but increases with increasing the width of density transition layer Dρ. After the initial transient period and before the vortex has been well formed, the linear growth rates, γv and γρ, vary with Dv and Dρ approximately in the following way, lnγv=a-bDv and γρ=c+eln Dρ (Dρ<DρE), where a, b, c and e are fitting parameters and DρE is the effective interaction width of density transition layer. When Dρ>DρE the linear growth rate γρ does not vary significantly any more. One can use the hybrid effects of velocity and density transition layers to stabilize the KHI. Our numerical simulation results are in general agreement with the analytical results [L. F. Wang, et al., Phys. Plasma 17, 042103 (2010)].