Research On Compressible Lattice Boltzmann Model And Simplified Distribution Function-based Flux Solver

After systematic study on the existing compressile lattice Boltzmann (LB) models, we construct aplatform to derive non-free parameter LB models. In our platform, it was proved that the particleinternal energy is independent of lattice velocity, and the use of one variable to represent the particleinternal energy in the compressible LB model is justified. By means of Chapman-Enskog expansion,one can prove that with the conservative forms of moments in our platform, the Navier-Stokes equationscan be recovered. Based on this platform, we developd five non-free parameter LB models, includingthree one-dimensional (1D) models D1Q3, D1Q4and D1Q5and two tow-dimensional (2D) modelsD2Q8and D2Q12.In order to avoid solving discrete velocity Boltzmann equation (DVBE) directly and improve thecomputational efficiency, we apply finite volume-based lattice Boltzmann method (FV-LBM) andutilize our non-free parameter LB models to simulate compressible flows. This thesis at first shows thedetails of FV-LBM of1D model, and then extends it to2D applications. Numerical results show that thepresent non-free parameter models are more suitable for flow simulation with high Mach number thansome existing models. Furthermore, since the Euler equation is solved in FV-LBM, the computationalefficiency of FV-LBM is equivalent to Roe solver and van Leer solver.In addition, we propose an inviscid compressible flux solver by means of circular function. Firstly,the circular function is derived from Maxwellian distribution function with assumption that all theparticles are concentrated on a circle. And then, the flux solver is constructed by using circular functionin place of Maxwellian distribution function. By this way, the complexity of those existing Maxwellianfunction-based gas kinetic schemes (GKS) is overcome and the computational efficiency is improved.By applying this flux solver, some supersonic flows are simulated successfully.