Accreditation to Supervise Research: Jeroen Wackers

Abstract:

Adaptive grid refinement is the technique of locally dividing the cells of an initial grid during a simulation, in order to produce a fine grid that is adapted to the problem being solved. In computational fluid dynamics, adaptive refinement has already been studied for a long time. However, the method can only reach its full potential if it is combined with all the other capabilities of modern flow solvers, to obtain unprecedented accuracy and efficiency for the simulation of complex, realistic flows.

This work concerns the development of such a solver with adaptivity. It studies the requirements for the adaptation method coming from the need to simulate complex physics and geometries, to be usable in daily academic and industrial practice, and to allow development over a long time. The work describes the grid refinement method implemented in the incompressible multifluid Navier-Stokes solver ISIS-CFD and describes how the design of the method has been shaped by these requirements.

The refinement kernel which performs the actual mesh modification must be flexible, easy to maintain, and efficient for parallel computation. To limit the number of cells created for three-dimensional simulations, refinement is performed anisotropically: cells can be divided in one or more directions separately. For good mesh quality, even the undoing of previous refinements must be performed anisotropically.

The refinement criterion is the part of the algorithm which decides where the mesh will be refined. In a refinement method that evolves over a long time and that is applied to a wide range of problems, it must be easy to implement different criteria. This, and the need to control anisotropic refinement, motivated the choice of metric tensors as a framework for the refinement criteria: fields of 3x3 symmetric tensors, whose eigenvalues and eigenvectors in each position indicate the locally desired cell size in different directions. Such real-valued criteria can be computed separately from the rest of the refinement algorithm, which makes it easy to change the criterion without modifying anything else.

For practical application of adaptive refinement, straightforward user guidelines are essential. A good test for these guidelines is scripting, i.e. automatic setup of computations. Scripted computations with free-surface based refinement are shown to be possible today.

To show that the presented grid refinement method fulfills its main purposes of improving physical analysis, simplifying computations, and working together with the other components of ISIS-CFD, several series of computations are presented. This work ends with a reflection on the future of adaptive simulation. User experience translated into adaptive algorithms can control other aspects of the simulation besides the mesh. The results is a solver of which adaptivity forms the heart, guiding it to optimal performance for complex flow simulation.

Committee members

• Frédéric ALAUZET (Directeur de Recherche, INRIA)
• David DARMOFAL (Professor, Massachusetts Institute of Technology)
• Charles HIRSCH (Professeur, Vrije Universiteit Brussel)
• François JAUBERTEAU (Professeur des Universités, Université de Nantes)
• Barry KOREN (Professor, Eindhoven University of Technology)
• Thomas RUNG (Professeur, Hamburg University of Technology)
• Michel VISONNEAU (Directeur de recherche CNRS, Ecole Centrale de Nantes)