格子ボルツマン法による圧縮性流れのシミュレーション

抄録

Simulation method for compressible flows by the lattice Boltzmann model is explained. Especially, the lattice BGK model with multi-speed particles for two-and three-dimensional flows is shown, and the relationship between the particles distribution function and the macroscopic quantities is described. The isotropic feature of the forth order tensor is shown to be necessary for the macroscopic governing equations. The Navier-Stokes equations of a compressible fluid are derivedfrom the lattice BGK equation. As a bench-mark test, the flow in a shock tube is performed, and the result agrees well with an analytical solution or that by the finite difference method. The aeolian tone emitted by a circular cylinder is also simulated, and a dipole emission of sound wave is detected synchronized with the Karman vortex street. The lattice BGK model for compressible fluids is shown to be one of powerful tool for simulation of gas flows.