A fully conservative Eulerian–Lagrangian method for a convection–diffusion problem in a solenoidal field

Handle URI:
http://hdl.handle.net/10754/597274
Title:
A fully conservative Eulerian–Lagrangian method for a convection–diffusion problem in a solenoidal field
Authors:
Arbogast, Todd; Huang, Chieh-Sen
Abstract:
Tracer transport is governed by a convection-diffusion problem modeling mass conservation of both tracer and ambient fluids. Numerical methods should be fully conservative, enforcing both conservation principles on the discrete level. Locally conservative characteristics methods conserve the mass of tracer, but may not conserve the mass of the ambient fluid. In a recent paper by the authors [T. Arbogast, C. Huang, A fully mass and volume conserving implementation of a characteristic method for transport problems, SIAM J. Sci. Comput. 28 (2006) 2001-2022], a fully conservative characteristic method, the Volume Corrected Characteristics Mixed Method (VCCMM), was introduced for potential flows. Here we extend and apply the method to problems with a solenoidal (i.e., divergence-free) flow field. The modification is a computationally inexpensive simplification of the original VCCMM, requiring a simple adjustment of trace-back regions in an element-by-element traversal of the domain. Our numerical results show that the method works well in practice, is less numerically diffuse than uncorrected characteristic methods, and can use up to at least about eight times the CFL limited time step. © 2010 Elsevier Inc.
Citation:
Arbogast T, Huang C-S (2010) A fully conservative Eulerian–Lagrangian method for a convection–diffusion problem in a solenoidal field. Journal of Computational Physics 229: 3415–3427. Available: http://dx.doi.org/10.1016/j.jcp.2010.01.009.
Publisher:
Elsevier BV
Journal:
Journal of Computational Physics
Issue Date:
May-2010
DOI:
10.1016/j.jcp.2010.01.009
Type:
Article
ISSN:
0021-9991
Sponsors:
This author was supported in part by US National Science Foundation Grant DM5-0713815 and the King Abdullah University of Science and Technology (KAUST) Academic Excellence Alliance program.
Appears in Collections:
Publications Acknowledging KAUST Support

Full metadata record

DC FieldValue Language
dc.contributor.authorArbogast, Todden
dc.contributor.authorHuang, Chieh-Senen
dc.date.accessioned2016-02-25T12:29:34Zen
dc.date.available2016-02-25T12:29:34Zen
dc.date.issued2010-05en
dc.identifier.citationArbogast T, Huang C-S (2010) A fully conservative Eulerian–Lagrangian method for a convection–diffusion problem in a solenoidal field. Journal of Computational Physics 229: 3415–3427. Available: http://dx.doi.org/10.1016/j.jcp.2010.01.009.en
dc.identifier.issn0021-9991en
dc.identifier.doi10.1016/j.jcp.2010.01.009en
dc.identifier.urihttp://hdl.handle.net/10754/597274en
dc.description.abstractTracer transport is governed by a convection-diffusion problem modeling mass conservation of both tracer and ambient fluids. Numerical methods should be fully conservative, enforcing both conservation principles on the discrete level. Locally conservative characteristics methods conserve the mass of tracer, but may not conserve the mass of the ambient fluid. In a recent paper by the authors [T. Arbogast, C. Huang, A fully mass and volume conserving implementation of a characteristic method for transport problems, SIAM J. Sci. Comput. 28 (2006) 2001-2022], a fully conservative characteristic method, the Volume Corrected Characteristics Mixed Method (VCCMM), was introduced for potential flows. Here we extend and apply the method to problems with a solenoidal (i.e., divergence-free) flow field. The modification is a computationally inexpensive simplification of the original VCCMM, requiring a simple adjustment of trace-back regions in an element-by-element traversal of the domain. Our numerical results show that the method works well in practice, is less numerically diffuse than uncorrected characteristic methods, and can use up to at least about eight times the CFL limited time step. © 2010 Elsevier Inc.en
dc.description.sponsorshipThis author was supported in part by US National Science Foundation Grant DM5-0713815 and the King Abdullah University of Science and Technology (KAUST) Academic Excellence Alliance program.en
dc.publisherElsevier BVen
dc.subjectAdvection-diffusionen
dc.subjectCellular flowen
dc.subjectCharacteristicsen
dc.subjectConvection-enhanced diffusionen
dc.subjectDivergence-free flowen
dc.subjectELLAMen
dc.subjectLocal conservationen
dc.titleA fully conservative Eulerian–Lagrangian method for a convection–diffusion problem in a solenoidal fielden
dc.typeArticleen
dc.identifier.journalJournal of Computational Physicsen
dc.contributor.institutionUniversity of Texas at Austin, Austin, United Statesen
dc.contributor.institutionNational Sun Yat-Sen University Taiwan, Kaohsiung, Taiwanen
kaust.grant.programAcademic Excellence Alliance (AEA)en
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