Abstract
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.
