Lattice Boltzmann Approach to High-Speed Compressible Flows

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 Tsutahara [Phys. Rev. E \textbf{69}, 056702 (2004)] 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.

Figs.11 and 12 in JPEG format. Int. J. Mod. Phys. C (to appear)

References in corpus (4)

• Finite difference lattice Boltzmann model with flux limiters for liquid-vapor systems
• Lattice Boltzmann versus Molecular Dynamics simulation of nano-hydrodynamic flows
• Stability and stabilisation of the lattice Boltzmann method: Magic steps and salvation operations
• Scaling and hydrodynamic effects in lamellar ordering

Cited by in corpus (9)

• Multiple-Relaxation-Time Lattice Boltzmann Approach to Compressible Flows with Flexible Specific-Heat Ratio and Prandtl Number
• Two-Dimensional Lattice Boltzmann Model For Compressible Flows With High Mach Number
• Polar coordinate lattice Boltzmann modeling of compressible flows
• Lattice BGK kinetic model for high speed compressible flows: hydrodynamic and nonequilibrium behaviors
• Lattice Boltzmann model for combustion and detonation
• Multiple-relaxation-time lattice Boltzmann model for compressible fluids
• Lattice Boltzmann model for ultra-relativistic flows
• Polar coordinate lattice Boltzmann kinetic modeling of detonation phenomena
• Three-dimensional discrete Boltzmann models for compressible flows in and out of equilibrium