Multigrid Method to Solve Free Surface Flows

In recent years، many different methods have been developed to simulate free surface flows coupled with moving bodies. In this paper، for simulating ship maneuver، VOF method (CICSAM) and also for coupling velocity field and pressure a fractional step method are used. To increase simulation accuracy، the mesh size should be significantly fine. Unfortunately، fine grid causes increase in simulation time. So، multigrid method was applied for solving the Poisson equation obtained in the Navier-Stokes equations، when using fractional step method. In that case، we generated some coarse grids، using agglomeration method، which needs implemention of a fully unstructured grid. To evaluate the accuracy of the algorithm، some test cases، such as two sided cavity، dam break with obstacle، and barge towing problem، as well as a comparison between V and W cycles in multigrid method have been studied. The results show that implementation of multigrid method can improve the performance of the computer code up to 100%. Moreover، W cycle behaves better than V cycle in most cases.