FAS Multigrid Method for SIMPLER Algorithm

Investigators: Laith Zori & Ganesh Rajagopalan

Sponsored by : AEEM Dept. @ ISU, Sandia National Laboratories

Summary

This work is motivated by the need to find an efficient way of accelerating the convergence of the current SIMPLER-based codes with minimum change to the structure of the original code which has been developed for rotor-body interactional flows and flow through wind turbines.

The study presents the details of the Full Approximation Storage (FAS) V-cycle multigrid method applied to the decoupled solution of the SIMPLER algorithm in an effort to accelerate the convergence of the incompressible, laminar, steady, 2-D Navier-Stokes equations.

The performance of the new FAS-SIMPLER algorithm is compared with the single grid SIMPLER algorithm using the classical driven cavity problem. The FAS-SIMPLER method is found to converge much faster than the single grid method. The efficiency of the FAS-SIMPLER is improved as the grid size is increased. Figure 1 shows the contours of the streamline function for the driven cavity problem at Reynolds number of 400. Figure 2 compares the convergence history between the single grid SIMPLER an the new FAS-SIMPLER scheme. The efficiency of the FAS-SIMPLER algorithm over the single grid SIMPLER algorithm is summaries in Figure 3 as the CPU time to convergence is plotted versus the number of grids control volumes.

The results provide an encouraging prospect for applying the new algorithm to more complex fluid flow where larger grid densities are required.

Figure 1: Steamline function in the driven cavity at Re=400

Figure 2: Comparisons of the convergence history between FAS-SIMPLER multigrid method and the single grid SIMPLER method at Re=400.

Figure 3: CPU times required to obtained a converged solution for the driven cavity problem