Flux Limiter Lattice Boltzmann Scheme Approach to Compressible Flows with Flexible Specific-Heat Ratio and Prandtl Number

Abstract

We further develop the lattice Boltzmann (LB) model [Physica A 382 (2007) 502] for compressible flows from two aspects. Firstly, we modify the Bhatnagar—Gross—Krook (BGK) collision term in the LB equation, which makes the model suitable for simulating flows with different Prandtl numbers. Secondly, the flux limiter finite difference (FLFD) scheme is employed to calculate the convection term of the LB equation, which makes the unphysical oscillations at discontinuities be effectively suppressed and the numerical dissipations be significantly diminished. The proposed model is validated by recovering results of some well-known benchmarks, including (i) The thermal Couette flow; (ii) One- and two-dimensional Riemann problems. Good agreements are obtained between LB results and the exact ones or previously reported solutions. The flexibility, together with the high accuracy of the new model, endows the proposed model considerable potential for tracking some long-standing problems and for investigating nonlinear nonequilibrium complex systems.