A note on the stability of cut cells and cell merging

Research output: Contribution to journalArticle

Abstract

Embedded boundary meshes may have cut cells of arbitrarily small volume which can lead to stability problems in finite volume computations with explicit time stepping. We show that time step constraints are not as strict as often believed. We prove this in one dimension for linear advection and the first order upwind scheme. Numerical examples in two dimensions demonstrate that this carries over to more complicated situations. This analysis sheds light on the choice of time step when using cell merging to stabilize the arbitrarily small cells that arise in embedded boundary schemes.

Original languageEnglish (US)
Pages (from-to)180-186
Number of pages7
JournalApplied Numerical Mathematics
Volume96
DOIs
StatePublished - Jul 10 2015

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Advection
Merging
Cell
Upwind Scheme
Time Stepping
Finite Volume
One Dimension
Two Dimensions
Mesh
First-order
Numerical Examples
Demonstrate

Keywords

  • Cell merging
  • Cut cell
  • Embedded boundary
  • Stability

ASJC Scopus subject areas

  • Applied Mathematics
  • Computational Mathematics
  • Numerical Analysis

Cite this

A note on the stability of cut cells and cell merging. / Berger, Marsha.

In: Applied Numerical Mathematics, Vol. 96, 10.07.2015, p. 180-186.

Research output: Contribution to journalArticle

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