### Sloshing in a Multi-Physics Parallel Programming Paradigm

#### Abstract

In this work, transient free surface flows of a viscous incompressible fluid are numerically solved through parallel computation. Transient free surface flows are boundary-value problems of moving type that involve geometrical non-linearities. In contrast to more conventional CFD problems, the computational flow domain is partially bounded by a free surface which is not known a priori, since its shape must be computed as part of the solution. In steady-flow the free surface is obtained by an iterative process, but when the free surface evolves with time the problem is more difficult, generating large distortions in the computational flow domain. The incompressible Navier-Stokes numerical solver is based on the finite element method with equal order elements for pressure and velocity (linear elements), and it uses a Streamline Upwind/Petrov-Galerkin (SUPG) scheme combined with a Pressure-Stabilizing/Petrov-Galerkin (PSPG) one. At each time step, the fluid equations are solved with constant pressure and null viscous traction conditions at the free surface and the velocities obtained in this way are used for updating the positions of the surface nodes. Then, a pseudo elastic problem is solved in the fluid domain in order to relocate the interior nodes so as to keep mesh distortion controlled. This has been implemented in PETSc-FEM by running two parallel instances of the code and exchanging information between them. Some numerical examples are presented. [Journal of Applied Mechanics (JAM-ASME) vol 73, pp. 1017-1025 (2006)]