Two-Dimensional Slope Limiters for Finite Volume Schemes on Non-Coordinate-Aligned Meshes

In this paper we develop a new limiter for linear reconstruction on non-coordinate-aligned meshes in two space dimensions, with focus on Cartesian embedded boundary grids. Our limiter is inherently two dimensional and linearity preserving. It separately limits the $x$ and $y$ components of the gradi...

Full description

Saved in:
Bibliographic Details
Published in:SIAM journal on scientific computing 2013-01, Vol.35 (5), p.A2163-A2187
Main Authors: May, Sandra, Berger, Marsha
Format: Article
Language:English
Subjects:
Algorithms
Boundaries
Computation
Linear programming
Mathematical analysis
Methods
Optimization
Oscillations
Scalars
Simplex method
Slopes
Two dimensional
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:In this paper we develop a new limiter for linear reconstruction on non-coordinate-aligned meshes in two space dimensions, with focus on Cartesian embedded boundary grids. Our limiter is inherently two dimensional and linearity preserving. It separately limits the $x$ and $y$ components of the gradient, as opposed to a scalar limiter which limits all components simultaneously with one scalar. The limiter is based on solving a tiny linear program (LP) on each cell, using a very efficient version of the simplex method. A variety of computational results on triangular and embedded boundary meshes are presented. They demonstrate that the LP limiter successfully removes oscillations and significantly increases solution accuracy compared to a scalar limiter. [PUBLICATION ABSTRACT]
ISSN:1064-8275
1095-7197
DOI:10.1137/120875624