A stable projection method for the incompressible Navier–Stokes equations on arbitrary geometries and adaptive Quad/Octrees

TitleA stable projection method for the incompressible Navier–Stokes equations on arbitrary geometries and adaptive Quad/Octrees
Publication TypeJournal Article
Year of Publication2015
AuthorsGuittet A, Theillard M, Gibou F
JournalJournal of Computational Physics
Volume292
Pagination215–238
Date Published07/2016
ISSN00219991
KeywordsAdaptive mesh refinement, CNSI/MRL, CSC, FBNS02, Gibou, ICB, Incompressible, Irregular domains, Keck, Level-set, MAC grid, Navier–Stokes, Quad/Octrees, Sharp, Stable projection method, Viscosity
Abstract

We present a numerical method for solving the incompressible Navier–Stokes equations on non-graded quadtree and octree meshes and arbitrary geometries. The viscosity is treated implicitly through a finite volume approach based on Voronoi partitions, while the convective term is discretized with a semi-Lagrangian scheme, thus relaxing the restrictions on the time step. A novel stable implementation of the projection step is introduced, making use of the Marker And Cell layout for the data. The solver is validated numerically in two and three spatial dimensions.

URLhttp://www.sciencedirect.com/science/article/pii/S0021999115001710
DOI10.1016/j.jcp.2015.03.024
Refereed DesignationRefereed
Grant: 
MRI R2 (CNS-0960316), CSC, MRL (DMR-1121053)