A Minimal Element Distortion Strategy for Computational Mesh Dynamics

Ezequiel López, Norberto Marcelo Nigro, Mario Alberto Storti, Jorge Toth


Mesh motion strategy is one of the key points in many
fluid-structure interaction (FSI) problems. Due to the increasing
application of FSI to solve the current challenging engineering
problems this topic has deserved a highlight interest. There are
several different strategies to solve this problem, some of them using
a discrete and lumped spring-mass system to propagate the boundary
motion into the volume mesh and many others using an elastostatic
problem to deform the mesh. In all these strategies there is always a
risk of producing an invalid mesh, a mesh with some elements inverted.
Normally this condition is irreversible and once an invalid mesh is
obtained it is difficult to continue. In this paper the mesh motion
strategy is defined as an optimization problem. By its definition this
strategy may be classified as a particular case of an elastostatic
problem where the material constitutive law is defined in terms of the
minimization of certain energy functional that takes into account the
degree of element distortion. Some advantages of this strategy is its
natural tendency to high quality meshes, its robustness and its
straightforward extension to 3D problems. Several examples included in
this paper show these capabilities. Even though this strategy seems
to be very robust it is not able to recover a valid mesh starting from
an invalid one. This improvement is left for future work.[International Journal for Numerical Methods in Engineering

Full Text: