Mesh optimization based on a Neo-Hookean hyperelasticity model
Loading...
Date
2023
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Abstract
For industrial applications CFD-simulations have become an important addition to experiments.
To perform them the underlying geometry has to be created on a computer
and embedded into a computational mesh. This mesh needs to meet certain quality criteria.
This mesh needs to meet certain quality criteria, which are not commonly met
by many conventional mesh-generation tool. However, automated tools are necessary to
simulate experiments with a time-dependent geometry, for example a rising bubble or
fluid-structure interaction.
In this thesis, we study the automatic optimization of a mesh by minimizing a neohookean
hyperelasticity model. The aim of our mesh optimization is to either smoothen
a mesh, or to adapt a mesh to a given geometry. In the first part of the thesis we propose a
specific energy model from this class and investigate if a solution to the minimization of
this specific energy exists or not.
To solve this minimization problem we need to develop an algorithm. After this we have
to investigate if this specific energy function fulfills all requirements of this algorithm.
The chosen algorithm is an adaptation of Newton’s method in a function space. To globalize
the convergence of Newton’s method we use operator-adaption techniques in a Hilbert
space. This makes the algorithm a Quasi-Newton-Method. We proceed to add other elements
that are known from optimization so that the algorithm becomes even more robust.
Finally we perform several numerical tests to investigate the performance of this method.
In our studies we find that for a certain set of parameters the solution of the minimization
problem exists. This set of parameters is limited, but the limits are reasonable for most
practical use-cases. During our numerical tests we find the method to be stable and robust
enough to automatically smoothen a mesh, but to adapt a given mesh to a given geometry
our results are unclear: For simulations in two dimensions, the developed method seems
to perform well and we get promising results with even just a type of Picard-iteration. For
simulations in three dimensions, some adaptations might be necessary and more tests are
required.