AMixed explicit implicit time stepping scheme for cartesian embedded boundary meshes

Sandra May, Marsha Berger

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

We present a mixed explicit implicit time stepping scheme for solving the linear advection equationMay, Sandra on a Cartesian embedded boundary mesh. The scheme represents a new approach for overcoming the small cell problem—that standard finite volume schemes are not stable on the arbitrarily small cut cells. It uses implicit time stepping on cut cells for stability. On standard Cartesian cells, explicit time stepping is employed. This keeps the cost small and makes it possible to extend existing schemes from Cartesian meshes to Cartesian embedded boundary meshes. The coupling is done by flux bounding, for which we can prove a TVD result. We present numerical results in one and two dimensions showing secondorder convergence in the L1norm and between first- and second-order convergence in the L∞ norm.

Original languageEnglish (US)
Title of host publicationFinite Volumes for Complex Applications VII - Methods and Theoretical Aspects, FVCA 7
EditorsChristian Rohde, Jürgen Fuhrmann, Mario Ohlberger
PublisherSpringer New York LLC
Pages393-400
Number of pages8
ISBN (Electronic)9783319056838
DOIs
StatePublished - 2014
Event7th International Symposium on Finite Volumes for Complex Applications-Problems and Perspectives, FVCA7 - Berlin, Germany
Duration: Jun 15 2014Jun 20 2014

Publication series

NameSpringer Proceedings in Mathematics and Statistics
Volume77
ISSN (Print)2194-1009
ISSN (Electronic)2194-1017

Other

Other7th International Symposium on Finite Volumes for Complex Applications-Problems and Perspectives, FVCA7
CountryGermany
CityBerlin
Period6/15/146/20/14

ASJC Scopus subject areas

  • Mathematics(all)

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  • Cite this

    May, S., & Berger, M. (2014). AMixed explicit implicit time stepping scheme for cartesian embedded boundary meshes. In C. Rohde, J. Fuhrmann, & M. Ohlberger (Eds.), Finite Volumes for Complex Applications VII - Methods and Theoretical Aspects, FVCA 7 (pp. 393-400). (Springer Proceedings in Mathematics and Statistics; Vol. 77). Springer New York LLC. https://doi.org/10.1007/978-3-319-05684-5_38