Simulation of shockwave propagation with a thermal lattice Boltzmann model

A two-dimensional 19-velocity (D2Q19) lattice Boltzmann model which satisfies the conservation laws governing the macroscopic and microscopic mass, momentum and energy with local equilibrium distribution order O(u^4) rather than the usual O(u^3) has been developed. This model is applied to simulate the reflection of shockwaves on the surface of a triangular obstacle. Good qualitative agreement between the numerical predictions and experimental measurements is obtained. As the model contains the higher-order terms in the local equilibrium distribution, it performs much better in terms of numerical accuracy and stability than the earlier 13-velocity models with the local equilibrium distribution accurate only up to the second order in the velocity u.