关键词:
Wind
摘要:
A review of existing solution procedures to solve steady and unsteady Navier-Stokes equations (NS) using multigrid methods and their relevance to computational wind engineering is discussed. Even though multigrid procedures for steady NS equations are robust;they are not preferable for many wind engineering applications due to their unsteady nature. Hence methods that are available for the solution of unsteady NS equations and when to prefer which procedure will be discussed. In CWE when time-dependent phenomena are investigated using large eddy simulation (LES), the most time consuming part is the solution of pressure equations. The pressure equation is solved thousands of times for many of the practical problems. Here flow around a circular cylinder and/or flow over a cube is considered for illustration to compare the performance of the multigrid (MG), preconditioned conjugate gradient (PCG) and MG-conjugate gradient (MGCG) solution procedures for the pressure equations. The different smoothers considered for MG and MGCG are Gauss-Siedel (GS), Incomplete Cholesky factorization (ILU), and line GS (LGS). It is found from this study that MGCG using ILU smoother is the most robust for the optimum storage. The pressure equations could be solved in about 5-V cycles or about 10 work units (WU). A WU is the amount of computational work required to perform one GS iteration. If more storage is available, one form PCG is the fastest. MG using ILU smoother is preferable when one wants to use less storage. For general applications and for easy programming PCG using ILU as the preconditioner is preferable.