シェル屋根面周辺の流れの三次元非圧縮性粘性流体解析へのマルチグリッド法の適用

概要

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An efficient linear solver using a multigrid method is developed for solving the pressure Poisson equation. The three-dimensional incompressible viscous fluid flow analysis is performed for investigating dynamic behaviors of a shell roof under strong wind. The improved balancing tensor diffusivity method and fractional step method (IBTD+FS method) combined with the finite element method is used for discretizing the Navier-Stokes equation. In this scheme, the pressure Poisson equation is solved implicitly. Solution process of the equation, which is a large-scale system of linear equations, is the most computationally expensive part. In order to improve the computation speed, a preconditioning technique based on a multigrid method for the conjugate gradient method (CG method) is employed. A simple formulation that combines the diagonal-scaling preconditioner and coarse grid correction is proposed. In addition, a finite element mesh for a two-dimensional analysis is used as a coarse grid for the three-dimensional analysis. The proposed method is implemented in the fluid flow analysis code. Performance study of the proposed method is conducted by solving a number of illustrative examples. Computation speed of the proposed method is much faster than the CG method with a simple diagonal-scaling preconditioner.
社団法人日本建築学会の論文
2007-08-30