Alexandria Digital Research Library

Simulation of incompressible viscous flows on distributed Octree grids

Author:
Guittet, Arthur
Degree Grantor:
University of California, Santa Barbara. Mechanical Engineering
Degree Supervisor:
Frederic Gibou
Place of Publication:
[Santa Barbara, Calif.]
Publisher:
University of California, Santa Barbara
Creation Date:
2016
Issued Date:
2016
Topics:
Applied mathematics
Keywords:
Adaptive
Navier-stokes
Parallel
Level-set
Voronoi
Octree
Genres:
Dissertations, Academic and Online resources
Dissertation:
Ph.D.--University of California, Santa Barbara, 2016
Description:

This dissertation focuses on numerical simulation methods for continuous problems with irregular interfaces. A common feature of these types of systems is the locality of the physical phenomena, suggesting the use of adaptive meshes to better focus the computational effort, and the complexity inherent to representing a moving irregular interface. We address these challenges by using the implicit framework provided by the Level-Set method and implemented on adaptive Quadtree (in two spatial dimensions) and Octree (in three spatial dimensions) grids. This work is composed of two sections.

In the first half, we present the numerical tools for the study of incompressible monophasic viscous flows. After a study of an alternative grid storage structure to the Quad/Oc-tree data structure based on hash tables, we introduce the extension of the level-set method to massively parallel forests of Octrees. We then detail the numerical scheme developed to attain second order accuracy on non-graded Quad/Oc-tree grids and demonstrate the validity and robustness of the resulting solver. Finally, we combine the fluid solver and the parallel framework together and illustrate the potential of the approach.

The second half of this dissertation presents the Voronoi Interface Method (VIM), a new method for solving elliptic systems with discontinuities on irregular interfaces such as the ones encountered when simulating viscous multiphase flows. The VIM relies on a Voronoi mesh built on an underlying Cartesian grid and is compact and second order accurate while preserving the symmetry and positiveness of the resulting linear system. We then compare the VIM with the popular Ghost Fluid Method before adapting it to the simulation of the problem of the electropermeabilization of cells.

Physical Description:
1 online resource (259 pages)
Format:
Text
Collection(s):
UCSB electronic theses and dissertations
ARK:
ark:/48907/f3sq90fd
ISBN:
9781369146011
Catalog System Number:
990046968470203776
Rights:
Inc.icon only.dark In Copyright
Copyright Holder:
Arthur Guittet
File Description
Access: Public access
Guittet_ucsb_0035D_12971.pdf pdf (Portable Document Format)