An unconditionally stable fully conservative semi-Lagrangian method

Handle URI:
http://hdl.handle.net/10754/597545
Title:
An unconditionally stable fully conservative semi-Lagrangian method
Authors:
Lentine, Michael; Grétarsson, Jón Tómas; Fedkiw, Ronald
Abstract:
Semi-Lagrangian methods have been around for some time, dating back at least to [3]. Researchers have worked to increase their accuracy, and these schemes have gained newfound interest with the recent widespread use of adaptive grids where the CFL-based time step restriction of the smallest cell can be overwhelming. Since these schemes are based on characteristic tracing and interpolation, they do not readily lend themselves to a fully conservative implementation. However, we propose a novel technique that applies a conservative limiter to the typical semi-Lagrangian interpolation step in order to guarantee that the amount of the conservative quantity does not increase during this advection. In addition, we propose a new second step that forward advects any of the conserved quantity that was not accounted for in the typical semi-Lagrangian advection. We show that this new scheme can be used to conserve both mass and momentum for incompressible flows. For incompressible flows, we further explore properly conserving kinetic energy during the advection step, but note that the divergence free projection results in a velocity field which is inconsistent with conservation of kinetic energy (even for inviscid flows where it should be conserved). For compressible flows, we rely on a recently proposed splitting technique that eliminates the acoustic CFL time step restriction via an incompressible-style pressure solve. Then our new method can be applied to conservatively advect mass, momentum and total energy in order to exactly conserve these quantities, and remove the remaining time step restriction based on fluid velocity that the original scheme still had. © 2011 Elsevier Inc.
Citation:
Lentine M, Grétarsson JT, Fedkiw R (2011) An unconditionally stable fully conservative semi-Lagrangian method. Journal of Computational Physics 230: 2857–2879. Available: http://dx.doi.org/10.1016/j.jcp.2010.12.036.
Publisher:
Elsevier BV
Journal:
Journal of Computational Physics
KAUST Grant Number:
42959
Issue Date:
Apr-2011
DOI:
10.1016/j.jcp.2010.12.036
Type:
Article
ISSN:
0021-9991
Sponsors:
Research supported in part by ONR N0014-06-1-0393, ONR N00014-06-1-0505, ONR N00014-09-1-0101, ONR N00014-11-1-0027, ONR N00014-05-1-0479 for a computing cluster, and King Abdullah University of Science and Technology (KAUST) 42959. J.G. was supported in part by, and computational resources were provided in part by ONR N00014-06-1-0505 and ONR N00014-09-C-015. M.L. was supported in part by an Intel Ph.D. Fellowship.
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Full metadata record

DC FieldValue Language
dc.contributor.authorLentine, Michaelen
dc.contributor.authorGrétarsson, Jón Tómasen
dc.contributor.authorFedkiw, Ronalden
dc.date.accessioned2016-02-25T12:41:47Zen
dc.date.available2016-02-25T12:41:47Zen
dc.date.issued2011-04en
dc.identifier.citationLentine M, Grétarsson JT, Fedkiw R (2011) An unconditionally stable fully conservative semi-Lagrangian method. Journal of Computational Physics 230: 2857–2879. Available: http://dx.doi.org/10.1016/j.jcp.2010.12.036.en
dc.identifier.issn0021-9991en
dc.identifier.doi10.1016/j.jcp.2010.12.036en
dc.identifier.urihttp://hdl.handle.net/10754/597545en
dc.description.abstractSemi-Lagrangian methods have been around for some time, dating back at least to [3]. Researchers have worked to increase their accuracy, and these schemes have gained newfound interest with the recent widespread use of adaptive grids where the CFL-based time step restriction of the smallest cell can be overwhelming. Since these schemes are based on characteristic tracing and interpolation, they do not readily lend themselves to a fully conservative implementation. However, we propose a novel technique that applies a conservative limiter to the typical semi-Lagrangian interpolation step in order to guarantee that the amount of the conservative quantity does not increase during this advection. In addition, we propose a new second step that forward advects any of the conserved quantity that was not accounted for in the typical semi-Lagrangian advection. We show that this new scheme can be used to conserve both mass and momentum for incompressible flows. For incompressible flows, we further explore properly conserving kinetic energy during the advection step, but note that the divergence free projection results in a velocity field which is inconsistent with conservation of kinetic energy (even for inviscid flows where it should be conserved). For compressible flows, we rely on a recently proposed splitting technique that eliminates the acoustic CFL time step restriction via an incompressible-style pressure solve. Then our new method can be applied to conservatively advect mass, momentum and total energy in order to exactly conserve these quantities, and remove the remaining time step restriction based on fluid velocity that the original scheme still had. © 2011 Elsevier Inc.en
dc.description.sponsorshipResearch supported in part by ONR N0014-06-1-0393, ONR N00014-06-1-0505, ONR N00014-09-1-0101, ONR N00014-11-1-0027, ONR N00014-05-1-0479 for a computing cluster, and King Abdullah University of Science and Technology (KAUST) 42959. J.G. was supported in part by, and computational resources were provided in part by ONR N00014-06-1-0505 and ONR N00014-09-C-015. M.L. was supported in part by an Intel Ph.D. Fellowship.en
dc.publisherElsevier BVen
dc.subjectCompressible flowen
dc.subjectConservative methodsen
dc.subjectIncompressible flowen
dc.titleAn unconditionally stable fully conservative semi-Lagrangian methoden
dc.typeArticleen
dc.identifier.journalJournal of Computational Physicsen
dc.contributor.institutionStanford University, Palo Alto, United Statesen
kaust.grant.number42959en
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