Parallel Implementation Of Free Surface Flows

Abstract

In this work, transient free surface flows of a viscous incompressible fluid are
numerically solved with a parallel computation. Transient free surface flows are boundaryvalue
problems of moving type that involves geometrical non-linearities. In contrast to
CFD more conventional 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
the problem is more difficult when the free surface evolves with time, generating large
distortions in the computational flow domain. In this work, an 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 Stabilized 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. 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 minimize mesh distortion.
This has been implemented in PETSc-FEM by running two parallel instances of the code
and exchanging information between them. A numerical example is presented.