格子ボルツマン法を用いた2次元移流拡散方程式の数値スキームに関する研究

抄録

We investigate stability and accuracy of the numerical scheme obtained from the lattice Boltzmann method (LBM) for numerical solutions of two-dimensional advection-diffusion equations. A system of explicit finite difference equations derived from the the lttice Boltzmann equation (LBE) based on the Bhatnagar, Gross and Krook (BGK) model for a 9-velocity model gives the numerical scheme. The stability regions of the scheme in various cases of the relaxation parameter ω in the LBE are found by numerically solving the eigenvalue problems of the amplification matrix of the scheme corresponding to each cases. In order to investigate the accuracy of the scheme, a benchmark problem is solved, and the explicit scheme based on the LBM is compared with traditional explicit and implicit schemes. The results of the numerical experiments show that the explicit schemes based on the LBM demonstrate comparable accuracy to the bilinear finite element scheme if the parameters appeared in the scheme are set as values in the stability reagion.