The incompressible Navier-Stokes equations constitute a transient, non-linear system which has well-known stability issues when the standard Galerkin finite element discretization is used. This means that some treatment will be required before we can implement their solution. We implement a solution strategy based on algebraic subgrid scale stabilization and a generalized Newmark method for iteration in time. This results in a linear system which, unfortunately, can be poorly scaled, as it involves both velocity and pressure degrees of freedom. As a result, the system is difficult to solve using iterative methods, which are preferable for large problems. To avoid this situation, we have used an uncoupling approach based on a Schur complement formulation for the pressure, which results in a scheme similar to that of fractional step methods.

Two different implementations of this method, one using OpenMP and another based on MPI through the Trilinos library, have been used to solve Ahmed's body, a standard benchmark problem in turbulence which simulates the flow around a bus-like object. Both implementations are compared with each other and with a scalar run of the same example, with emphasis on performance gains provided by the parallelization.

In this sense, we have found that the time benefit obtained from the parallelization is affected by the hardware where the simulations are run. In our case, this imposes us two clear restrictions: OpenMP is limited to processors that can access some shared memory, and in general the performance is affected by competition between the processes for memory access, which seems to be an important bottleneck in our test system. In general, it can be said that, when choosing an approach to parallelization, it is important to take into account the available hardware.

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