An Explicit Implicit Scheme for Cut Cells in Embedded Boundary Meshes

Sandra May, Marsha Berger

Research output: Contribution to journalArticle

Abstract

We present a new mixed explicit implicit time stepping scheme for solving the linear advection equation on a Cartesian cut cell mesh. We use a standard second-order explicit scheme on Cartesian cells away from the embedded boundary. On cut cells, we use an implicit scheme for stability. This approach overcomes the small cell problem—that standard schemes are not stable on the arbitrarily small cut cells—while keeping the cost fairly low. We examine several approaches for coupling the schemes in one dimension. For one of them, which we refer to as flux bounding, we can show a TVD result for using a first-order implicit scheme. We also describe a mixed scheme using a second-order implicit scheme and combine both mixed schemes by an FCT approach to retain monotonicity. In the second part of this paper, extensions of the second-order mixed scheme to two and three dimensions are discussed and the corresponding numerical results are presented. These indicate that this mixed scheme is second-order accurate in (Formula presented.) and between first- and second-order accurate along the embedded boundary in two and three dimensions.

Original languageEnglish (US)
Pages (from-to)1-25
Number of pages25
JournalJournal of Scientific Computing
DOIs
StateAccepted/In press - Dec 3 2016

Fingerprint

Explicit Scheme
Implicit Scheme
Mesh
Cell
Advection
Fluxes
Cartesian
Three-dimension
Two Dimensions
Costs
First-order
Advection Equation
Time Stepping
One Dimension
Monotonicity
Linear equation
Numerical Results

Keywords

  • Cartesian cut cell method
  • Embedded boundary grid
  • Explicit implicit scheme
  • Finite volume scheme
  • Small cell problem

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Software
  • Engineering(all)
  • Computational Theory and Mathematics

Cite this

An Explicit Implicit Scheme for Cut Cells in Embedded Boundary Meshes. / May, Sandra; Berger, Marsha.

In: Journal of Scientific Computing, 03.12.2016, p. 1-25.

Research output: Contribution to journalArticle

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