A high order characteristic discontinuous Galerkin scheme for advection on unstructured meshes

Lee, David Robert; Lowrie, Robert Byron; Petersen, Mark Roger; Ringler, Todd Darwin; Hecht, Matthew W.

doi:10.1016/j.jcp.2016.08.010

Title: A high order characteristic discontinuous Galerkin scheme for advection on unstructured meshes

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Abstract

A new characteristic discontinuous Galerkin (CDG) advection scheme is presented. In contrast to standard discontinuous Galerkin schemes, the test functions themselves follow characteristics in order to ensure conservation and the edges of each element are also traced backwards along characteristics in order to create a swept region, which is integrated in order to determine the mass flux across the edge. Both the accuracy and performance of the scheme are greatly improved by the use of large Courant–Friedrichs–Lewy numbers for a shear flow test case and the scheme is shown to scale sublinearly with the number of tracers being advected, outperforming a standard flux corrected transport scheme for 10 or more tracers with a linear basis. Moreover the CDG scheme may be run to arbitrarily high order spatial accuracy and on unstructured grids, and is shown to give the correct order of error convergence for piecewise linear and quadratic bases on regular quadrilateral and hexahedral planar grids. Using a modal Taylor series basis, the scheme may be made monotone while preserving conservation with the use of a standard slope limiter, although this reduces the formal accuracy of the scheme to first order. The second order scheme is roughly as accurate asmore »« less

Authors:

Lee, David Robert ^[1];

^[1];

^[1]

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

Publication Date:: Fri Aug 12 00:00:00 EDT 2016

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

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

OSTI Identifier:: 1460624

Alternate Identifier(s):: OSTI ID: 1359304

Report Number(s):: LA-UR-16-22694
Journal ID: ISSN 0021-9991; TRN: US1901880

Grant/Contract Number:: AC52-06NA25396; LA-UR-16-22694

Resource Type:: Accepted Manuscript

Journal Name:: Journal of Computational Physics

Additional Journal Information:: Journal Volume: 324; Journal Issue: C; Journal ID: ISSN 0021-9991

Publisher:: Elsevier

Country of Publication:: United States

Language:: English

Subject:: 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Mathematics; Discontinuous Galerkin; Advection equation; High order advection; Lagrangian characteristics; Unstructured mesh

Citation Formats


                    Lee, David Robert, Lowrie, Robert Byron, Petersen, Mark Roger, Ringler, Todd Darwin, and Hecht, Matthew W. A high order characteristic discontinuous Galerkin scheme for advection on unstructured meshes.  United States: N. p., 2016. 
Web.  doi:10.1016/j.jcp.2016.08.010.

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                    Lee, David Robert, Lowrie, Robert Byron, Petersen, Mark Roger, Ringler, Todd Darwin, & Hecht, Matthew W. A high order characteristic discontinuous Galerkin scheme for advection on unstructured meshes.  United States.  https://doi.org/10.1016/j.jcp.2016.08.010

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                    Lee, David Robert, Lowrie, Robert Byron, Petersen, Mark Roger, Ringler, Todd Darwin, and Hecht, Matthew W. Fri .  
"A high order characteristic discontinuous Galerkin scheme for advection on unstructured meshes".  United States.  https://doi.org/10.1016/j.jcp.2016.08.010.  https://www.osti.gov/servlets/purl/1460624.

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@article{osti_1460624,

  title        = {A high order characteristic discontinuous Galerkin scheme for advection on unstructured meshes},

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

  abstractNote = {A new characteristic discontinuous Galerkin (CDG) advection scheme is presented. In contrast to standard discontinuous Galerkin schemes, the test functions themselves follow characteristics in order to ensure conservation and the edges of each element are also traced backwards along characteristics in order to create a swept region, which is integrated in order to determine the mass flux across the edge. Both the accuracy and performance of the scheme are greatly improved by the use of large Courant–Friedrichs–Lewy numbers for a shear flow test case and the scheme is shown to scale sublinearly with the number of tracers being advected, outperforming a standard flux corrected transport scheme for 10 or more tracers with a linear basis. Moreover the CDG scheme may be run to arbitrarily high order spatial accuracy and on unstructured grids, and is shown to give the correct order of error convergence for piecewise linear and quadratic bases on regular quadrilateral and hexahedral planar grids. Using a modal Taylor series basis, the scheme may be made monotone while preserving conservation with the use of a standard slope limiter, although this reduces the formal accuracy of the scheme to first order. The second order scheme is roughly as accurate as the incremental remap scheme with nonlocal gradient reconstruction at half the horizontal resolution. Furthermore, the scheme is being developed for implementation within the Model for Prediction Across Scales (MPAS) Ocean model, an unstructured grid finite volume ocean model.},

  doi          = {10.1016/j.jcp.2016.08.010},

  journal      = {Journal of Computational Physics},

  number       = C,

  volume       = 324,

  place        = {United States},

  year         = {Fri Aug 12 00:00:00 EDT 2016},

  month        = {Fri Aug 12 00:00:00 EDT 2016}

}

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