Lattice Boltzmann Method for high Reynolds number compressible flow

We employ a Lattice Boltzmann Method (LBM) for modelling high Reynolds number (Re) compressible supersonic flow using D2Q9 lattice. In this model, a two -population thermal lattice Boltzmann (LB) is utilized in order to allow varying Prandtl number and adiabatic exponent. The equilibrium population f(i)(eq) term for mass and momentum conservation is matched analytically with order of accuracy O(Ma(4)), while the equilibrium population g(i)(eq )term for energy conservation is solved numerically through Lagrange multipliers method. By using more accurate equilibrium population g(i)(eq), the present numerical method shows the enhancement of stability, especially at high Reynolds and Mach number flows. To simulate high Reynolds and Mach number (Ma) flows efficiently, we adopt a shifted lattice scheme, stabilized by relaxation time depending on the Knudsen number. The LBM show excellent accuracy through 1D Riemann examples, capable of handling expansion shock waves and discontinuity. Our results for supersonic flow past a cylinder also find excellent agreement with experimental data in literature. Separately, we benchmark results for transonic and supersonic flows past a NACA0012 aerofoil as a demonstration of its simplicity, versatility for applications involving high Reynolds and Mach numbers (Ma(infinity) = 1.5, Re = 10(7)).