1602 分布関数の空間微分に関する格子ボルツマン方程式を用いた圧縮性流体解析(S35-1 圧縮性流れの基礎と応用(1),S35 圧縮性流れの基礎と応用)

Abstract

Spatial derivative of the distribution function follows the lattice Boltzmann equation (LBE), because the advection term in the kinetic equation is linear in the lattice Boltzmann method (LBM). The Cubic Interpolated Propagation Method is employed to discretize the kinetic equation for spatial derivative. We investigate the approximation accuracy of the LBE with the CIP method by simulations of shock tube problems of Sod and of Lax. The simulation results of the shock tube problems reveal that the CIP method is applicable to the LBE for compressible flow, and the differentiations of fluid density, velocity, and energy are able to be calculated by a simple arithmetic calculation of the spatial derivative of the distribution function. Because the numerical diffusion of the LBE with the CIP method is larger than that of the conventional LBM, the CIP method suppresses the numerical oscillations in the vicinity of sharp discontinuities in the simulations of the shock tube.