ACCURACY ANALYSIS OF LATTICE BOLTZMANN METHOD FOR THE POISSON EQUATION

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  • ポアソン方程式に対する格子ボルツマン法の精度評価
  • ポアソン ホウテイシキ ニ タイスル コウシ ボルツマンホウ ノ セイド ヒョウカ

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This paper analyzes the accuracy of two-dimensional lattice Boltzmann method (LBM) for the Poisson equation. By modifying the forcing term and the definition of the physical quantity, the LBM eliminates the error term depending on the relaxation time. The calculations for the Poisson equation with sinusoidal source show that the LBM obtains the second order convergence rate in space and that there is good agreement between the numerical and the analytical solutions. I investigate the computational efficiency by comparative study with the finite difference method (FDM) including the Jacobi, the Gauss-Seidel, and the SOR methods. The computational results for the Helmholtz equation make clear that the approximate relaxation time makes the LBM faster than the SOR method, or more accurate than the FDM. In addition, there is a trade-off between the efficiency and the accuracy provided by the adjustment of the relaxation time in the LBM.

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