On the use of conservative formulation of energy equation in hybrid compressible lattice Boltzmann method

Effect of density variations on mass conservation properties is widely recognized in the lattice Boltzmann method (LBM), thus non-conservative form scalar transport equation was commonly adopted within framework hybrid LBM. Focusing compressible LBM, and its effect energy are studied this paper. Starting from analysis law recovered by consistency between conservative formulations based various thermodynamic variables addressed. Driven theoretical analysis, a set modified consistent equations entropy internal derived to reduce error terms improve consistency. The intensively evaluated several numerical test cases, e.g., isentropic vortex convection, three-dimensional Taylor-Green shock-vortex interaction.