Multigrid Acceleration Of The Simpler Algorithm

Literatures on the applications of multigrid method in SIMPLE(Semi-Implicit Method for Pressure Linked Equations) algorithm and its novel variants such as SIMPLEC(SIMPLE consistent), SIMPLESSE and SIMPLESSEC are always available in academic publications. otherwise little work has been done on the application of multigrid method in SIMPLER algorithm which has some designed convergence properties. In this paper, based on the two-dimensional lid-driven cavity flow, the acceleration properties of multigrid method is studied when it is applied to solve the Navier-Stokes equations in conjunction with SIMPLER algorithm. The comparisons of acceleration properties of V-cycle and W-cycle multigrid methods as applied to SIMPLER algorithm are conducted qualitatively and quantitatively under different Reynolds numbers. The influence of grid hierarchy number on the acceleration quality of multigrid is investigated as well.From the practice of numerical solution of Navier-Stokes equation by SIMPLER algorithm together with multigrid, some conclusions can be drawn as follows: Firstly, multigrd method has good smoothing properties when it is applied to SIMPLER algorithm just as to SIMPLE algorithm and other variants.Secondly, the W-cycle multigrid method takes less steps of iterative procedure than the V-cycle version for the same Reynolds and accuracy request. W-cycle takes less work units than the V-cycle because of the complete elimination of the long wave error components in the process of W-cycle.Thirdly, the convergence is accelerated but not obviously with the increasing of grid hierarchy number, and we can not depend on the increasing of grid hierarchy number to achieve a well-convergent process because improvement of the efficiency of multigrid method lies in the practical mend during the implementation itself than in the grid hierarchy number.