密度流の数値解析における圧力計算の前処理法

Abstract

非圧縮性の密度流の数値計算を行う場合，圧力ポアソン方程式に効果的な前処理を利用することは，計算時間を短縮する上で重要である．また，非圧縮性流体の圧力計算手法である C-HSMAC 法では，圧力ポアソン方程式の求解を繰り返し行うことで，妥当な計算結果を得る上で重要な非圧縮条件を高精度に満足するように制御できる．本論文では，C-HSMAC 法における圧力ポアソン方程式の求解に前処理付き Bi-CGSTAB 法を用い，その効果について考察した．その結果，前処理により計算時間が短縮されることが確認できた．特に，Multigrid 法を前処理として用いた場合に，C-HSMAC 法の反復回数が他の解法と比べて大幅に少なくなるケースが存在しており，この現象も計算時間の短縮につながっていると考えられる．

When performing numerical calculations of incompressible density currents, it is important to use effective preconditioning for the pressure Poisson equation in order to reduce computation time. In the C-HSMAC method, which is a fluid calculation method, the incompressibility condition, which is important for obtaining valid calculation results, can be satisfied with high accuracy by iteratively solving the pressure Poisson equation at each time step. In this paper, the effect of using preconditioned Bi-CGSTAB methods for solving the pressure Poisson equation in the C-HSMAC method is discussed. As a result, it was confirmed that the preconditioning can reduce the computation time. In some cases, the number of iterations of the C-HSMAC method was smaller than that of other methods when the Multigrid method was used as a preconditioner. It is possible to expect not only a reduction in the computation time for a single iteration of the pressure Poisson equation, but also a reduction in the computation time due to the reduced number of iterations of the C-HSMAC method.