Tracer transport within an unstructured grid ocean model using characteristic discontinuous Galerkin advection

Lee, David Robert; Petersen, Mark Roger; Lowrie, Robert Byron; Ringler, Todd Darwin

doi:10.1016/j.camwa.2018.09.024

Title: Tracer transport within an unstructured grid ocean model using characteristic discontinuous Galerkin advection

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Abstract

In a previous article a characteristic discontinuous Galerkin (CDG) advection scheme was presented for tracer transport (Lee et al., 2016). The scheme is conservative, unconditionally stable with respect to time step and scales sub-linearly with the number of tracers being advected. Here in this paper, we present the implementation of the CDG advection scheme for tracer transport within MPAS-Ocean, a Boussinesque unstructured grid ocean model with an arbitrary Lagrangian Eulerian vertical coordinate. The scheme is implemented in both the vertical and horizontal dimensions, and special care is taken to ensure that the scheme remains conservative in the context of moving vertical layers. Consistency is ensured with respect to the dynamics by a renormalization of the fluxes with respect to the volume fluxes derived from the continuity equation. For spherical implementations, the intersection of the flux swept regions and the Eulerian grid are determined for great circle arcs, and the fluxes and element assembly are performed on the plane via a length preserving projection. Lastly, solutions are presented for a suite of test cases and comparisons made to the existing flux corrected transport scheme in MPAS-Ocean.

Authors:

Lee, David Robert ^[1];

^[2];

^[2]

Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Monash Univ., Melbourne, VIC (Australia)
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

Publication Date:: 2018-09-27

Research Org.:: Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

Sponsoring Org.:: USDOE Office of Science (SC), Biological and Environmental Research (BER); USDOE National Nuclear Security Administration (NNSA)

OSTI Identifier:: 1477647

Alternate Identifier(s):: OSTI ID: 1636880

Report Number(s):: LA-UR-17-22608
Journal ID: ISSN 0898-1221

Grant/Contract Number:: AC52-06NA25396; LA-UR-17-22608

Resource Type:: Accepted Manuscript

Journal Name:: Computers and Mathematics with Applications (Oxford)

Additional Journal Information:: Journal Name: Computers and Mathematics with Applications (Oxford); Journal Volume: 78; Journal Issue: 2; Conference: MultiMat, Santa Fe, NM (United States), 18-22 Sep 2017; Journal ID: ISSN 0898-1221

Publisher:: Elsevier

Country of Publication:: United States

Language:: English

Subject:: 97 MATHEMATICS AND COMPUTING; Discontinuous Galerkin; Semi Lagrangian; Advection equation; Unstructured grid; Arbitrary Lagrangian Eulerian vertical coordinate

Citation Formats


                    Lee, David Robert, Petersen, Mark Roger, Lowrie, Robert Byron, and Ringler, Todd Darwin. Tracer transport within an unstructured grid ocean model using characteristic discontinuous Galerkin advection.  United States: N. p., 2018. 
Web.  doi:10.1016/j.camwa.2018.09.024.

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                    Lee, David Robert, Petersen, Mark Roger, Lowrie, Robert Byron, & Ringler, Todd Darwin. Tracer transport within an unstructured grid ocean model using characteristic discontinuous Galerkin advection.  United States.  https://doi.org/10.1016/j.camwa.2018.09.024

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                    Lee, David Robert, Petersen, Mark Roger, Lowrie, Robert Byron, and Ringler, Todd Darwin. Thu .  
"Tracer transport within an unstructured grid ocean model using characteristic discontinuous Galerkin advection".  United States.  https://doi.org/10.1016/j.camwa.2018.09.024.  https://www.osti.gov/servlets/purl/1477647.

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@article{osti_1477647,

  title        = {Tracer transport within an unstructured grid ocean model using characteristic discontinuous Galerkin advection},

  author       = {Lee, David Robert and Petersen, Mark Roger and Lowrie, Robert Byron and Ringler, Todd Darwin},

  abstractNote = {In a previous article a characteristic discontinuous Galerkin (CDG) advection scheme was presented for tracer transport (Lee et al., 2016). The scheme is conservative, unconditionally stable with respect to time step and scales sub-linearly with the number of tracers being advected. Here in this paper, we present the implementation of the CDG advection scheme for tracer transport within MPAS-Ocean, a Boussinesque unstructured grid ocean model with an arbitrary Lagrangian Eulerian vertical coordinate. The scheme is implemented in both the vertical and horizontal dimensions, and special care is taken to ensure that the scheme remains conservative in the context of moving vertical layers. Consistency is ensured with respect to the dynamics by a renormalization of the fluxes with respect to the volume fluxes derived from the continuity equation. For spherical implementations, the intersection of the flux swept regions and the Eulerian grid are determined for great circle arcs, and the fluxes and element assembly are performed on the plane via a length preserving projection. Lastly, solutions are presented for a suite of test cases and comparisons made to the existing flux corrected transport scheme in MPAS-Ocean.},

  doi          = {10.1016/j.camwa.2018.09.024},

  journal      = {Computers and Mathematics with Applications (Oxford)},

  number       = 2,

  volume       = 78,

  place        = {United States},

  year         = {2018},

  month        = {9}

}

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