Development and Comparative Studies of Three Non-Free Parameter Lattice Boltzmann Models for Simulation of Compressible Flows (Advances in Applied Mathematics and Mechanics, 2012)
This paper at first shows the details of finite volume-based lattice Boltzmannmethod (FV-LBM) for simulation of compressible flows with shock waves. In theFV-LBM, the normal convective flux at the interface of a cell is evaluated byusing one-dimensional compressible lattice Boltzmann model, while the tangentialflux is calculated using the same way as used in the conventional Euler solvers.The paper then presents a platform to construct one-dimensional compressiblelattice Boltzmann model for its use in FV-LBM. The platform is formed from theconservation forms of moments. Under the platform, both the equilibriumdistribution functions and lattice velocities can be determined, andtherefore, non-free parameter model can be developed. The paper particularlypresents three typical non-free parameter models, D1Q3, D1Q4 and D1Q5. Theperformances of these three models for simulation of compressible flows areinvestigated by a brief analysis and their application to solve someone-dimensional and two-dimensional test problems. Numerical resultsshowed that D1Q3 model costs the least computation time and D1Q4 and D1Q5models have the wider application range of Mach number. From the results,it seems that D1Q4 model could be the best choice for the FV-LBM simulationof hypersonic flows.