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 L<sup>1</sup>norm 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
PublisherSpringer New York LLC
Pages393-400
Number of pages8
Volume77
ISBN (Print)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

Other

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

Fingerprint

Time Stepping
Cartesian
Mesh
Cell
L1-norm
Finite Volume Scheme
Advection
One Dimension
Two Dimensions
First-order
Norm
Numerical Results
Costs
Standards

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

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

AMixed explicit implicit time stepping scheme for cartesian embedded boundary meshes. / May, Sandra; Berger, Marsha.

Finite Volumes for Complex Applications VII - Methods and Theoretical Aspects, FVCA 7. Vol. 77 Springer New York LLC, 2014. p. 393-400.

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

May, S & Berger, M 2014, AMixed explicit implicit time stepping scheme for cartesian embedded boundary meshes. in Finite Volumes for Complex Applications VII - Methods and Theoretical Aspects, FVCA 7. vol. 77, Springer New York LLC, pp. 393-400, 7th International Symposium on Finite Volumes for Complex Applications-Problems and Perspectives, FVCA7, Berlin, Germany, 6/15/14. https://doi.org/10.1007/978-3-319-05684-5_38
May S, Berger M. AMixed explicit implicit time stepping scheme for cartesian embedded boundary meshes. In Finite Volumes for Complex Applications VII - Methods and Theoretical Aspects, FVCA 7. Vol. 77. Springer New York LLC. 2014. p. 393-400 https://doi.org/10.1007/978-3-319-05684-5_38
May, Sandra ; Berger, Marsha. / AMixed explicit implicit time stepping scheme for cartesian embedded boundary meshes. Finite Volumes for Complex Applications VII - Methods and Theoretical Aspects, FVCA 7. Vol. 77 Springer New York LLC, 2014. pp. 393-400
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