### A Minimal Element Distortion Strategy for Computational Mesh Dynamics

#### Abstract

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

(accepted)]

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

(accepted)]