Two-dimensional slope limiters for finite volume schemes on non-coordinate-aligned meshes

Sandra May, Marsha Berger

Research output: Contribution to journalArticle

Abstract

In this paper we develop a new limiter for linear reconstruction on non-coordinatealigned 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.

Original languageEnglish (US)
Pages (from-to)A2163-A2187
JournalSIAM Journal on Scientific Computing
Volume35
Issue number5
DOIs
StatePublished - 2013

Keywords

  • Cartesian cut cell method
  • Finite volume scheme
  • Linear programming
  • Slope limiter

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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