### 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.

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.

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Güemes 3450

S3000GLN Santa Fe, Argentina

Phone: 54-342-4511594 / 4511595 Int. 1006

Fax: 54-342-4511169

E-mail: amca(at)santafe-conicet.gov.ar

**Asociación Argentina de Mecánica Computacional**Güemes 3450

S3000GLN Santa Fe, Argentina

Phone: 54-342-4511594 / 4511595 Int. 1006

Fax: 54-342-4511169

E-mail: amca(at)santafe-conicet.gov.ar

**ISSN 2591-3522**