2007/06/04 by Xiaofei Pan, X. F. Pan, Aiguo Xu +2 · 1 citation
Engineering · Mathematics · Physics and Astronomy · #Applied mathematics #Compressibility #Compressible flow #Computational Fluid Dynamics and Aerodynamics #Computer science #Dissipation #Finite volume method #Fluid Dynamics and Turbulent Flows #HPP model #Lattice Boltzmann Simulation Studies #Lattice Boltzmann methods #Mach number #Mathematical analysis #Mathematics #Mechanics #Numerical analysis #Numerical stability #Physics #Reynolds number #Riemann solver #Stability (learning theory) #Statistical physics #Thermodynamics #Von Neumann architecture #Von Neumann stability analysis #cond-mat.soft #cond-mat.stat-mech
paper · pdf · doi:10.1142/s0129183107011716
published as International Journal of Modern Physics C Vol.18, No.11 (2007) 1747-1764. · Figs.11 and 12 in JPEG format. Int. J. Mod. Phys. C (to appear)
arxiv created 2007/06/04 · openalex publication_date 2007/11/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We present an improved lattice Boltzmann model for high-speed compressible flows. The model is composed of a discrete-velocity model by Kataoka and Tsutahara 15 and 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.