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 become of great interest. There are several different strategies to solve this problem, some of them use a discrete and lumped spring-mass system to propagate the boundary motion into the volume mesh, and many others use an elastostatic problem to deform the mesh. In all these strategies there is always risk of producing an invalid mesh, i.e. 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 can 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 are 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. Figure 20. Deformed mesh.Non-slip boundary conditions were imposed at the channel walls. The mesh used has 12K triangular elements and 6.7K nodes. Maximum channel blockage: 38%.In the original problem the maximum blockage of the channel is defined as 38% [33]. Figures 23-25 show the pressure, the velocity vector field and the velocity magnitude, respectively, at t * = 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9 and 1.0. In these figures only the domain region downstream to the indentation is included due to the fact that the

Numerical Modeling and Experimental Validation of Free Surface Flow Problems

“…stiffening criteria oriented to preserve the mesh in refined areas [117,196,229], or a neo-Hookean model [68]. -Minimization of a mesh-distortion measure [30,68], that have been developed for interface tracking specifically, or for computational mesh dynamics in general, as in [140,141].…”

Fluid–structure interaction study of the start-up of a rocket engine nozzle

“…[13]) or minimizing a functional that measures the distortion of the mesh with a geometric quality indicator (see Ref. [14]) through a separate PETSc-FEM parallel process. Both schemes are available in the PETSc-FEM code.…”

Mesh motion approach based on spring analogy method for unstructured meshes

“…Over the last decade technological development in many scientific and engineering applications including, to name only a few, blood flow circulation, parachute dynamics, airfoil oscillations, flutter prediction, fighter tail buffeting, gate sliding and a large class of freesurface flow problems, has placed emphasis on fluidstructure interaction (FSI) problems [1] . Mesh motion strategy is one of the key points in this kind of problems.…”