Free-Surface Flows In A Multi-Physics Programming Paradigm

Abstract

Unsteady free surface flows of an incompressible and viscous fluid are numerically solved by a finite element computation. In a previous communication (e.g. see Battaglia1 et al.), a mesh-movement technique was addressed for flow domains with a transient free surface of a viscous and incompressible fluid. The combined fluid and mesh moving problem was solved within the picture of a multi-physics programming paradigm, and was implemented reusing preexistent fluid and linear pseudo-elastic modules which were not specifically oriented to the free surface case. The "dialog" (data exchange and synchronization) between the fluid and pseudo-elastic solvers was performed by means of "hooks". These were C++ modules (or shell scripts like bash, Perl or Python) that run at certain specific points in the program. Nevertheless, when the free surface performs non-small displacements, there can be a numerical breakdown at some mesh update due to larger distortions in some elements close to the solid boundaries. The larger distortions are related to the non-slip boundary conditions imposed in some portion of the boundary. The objective of this work is to employ the non-linear pseudo-elastic formulation for the mesh-movement proposed by López 2 et al. in order to reduce mesh distortions and thus simulate larger free surface displacements.