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How to Choose the Best Pressure Solver for Your Application

There are several options for the iterative solution of pressures-velocities. How do I decide which option to use?

Users have the option of three basic solvers for coupling pressures and velocities; the Successive-Over-Relaxation (SOR) method, an Alternating-Direction-Implicit (ADI) method and a Generalized-Minimum-Residual (GMRES) method. Each method has advantages and disadvantages, but all should give satisfactory results if they converge.

An iterative solution is needed only for incompressible flow simulations and reflects the physical requirement that sound waves must travel over the entire computational domain to insure the incompressibility condition. Iterations allow all regions of a flow to remain in communication (i.e., to effectively have a high speed of sound) during each solution time step.

Selection of a solution option to give the best performance depends strongly on the type of problem being solved. For instance, the SOR method is the simplest and has the least requirement for additional memory. This scheme is very good at making pressure-velocity adjustment over small distances, but very poor at making adjustments that span distances comparable to the computational grid. On the other hand, the GMRES method is more computational intensive and requires substantial additional memory, but it is almost guaranteed to produce a solution with a high order of convergence. The ADI method is intermediate between the other options, requiring more computational work and memory than the SOR method, but it is not as robust at the GMRES method.

Let’s consider some examples from metal casting applications. For high-pressure-die casting the default SOR method usually works quite well. However, for a slowly poured gravity casting, liquid metal forms a pool in the bottom of the mold whose depth increases with time. In this case, the hydrostatic pressure in the pool is constantly changing because of the increasing depth and this situation is not the best for the SOR method, which does not do well with large scale pressure changes.

In general, it is recommended that users accept the simple SOR default option, unless they are certain that one of the more advanced techniques will be required. Then, if pressure-velocity iterations appear to hold back the solution process, the solution can be restarted with a different option. There is no a priori way to determine the best option—some experimentation may be required.