Reducing spurious mesh motion in Lagrangian finite volume and discontinuous Galerkin hydrodynamic methods

Morgan, Nathaniel Ray; Liu, Xiaodong; Burton, Donald E.

doi:10.1016/j.jcp.2018.06.008

Title: Reducing spurious mesh motion in Lagrangian finite volume and discontinuous Galerkin hydrodynamic methods

Abstract

The Lagrangian finite volume (FV) cell-centered hydrodynamic (CCH) method and the Lagrangian discontinuous Galerkin (DG) CCH method have been demonstrated to be quite stable and capable of producing very accurate solutions on many mesh topologies. However, some challenges can arise with higher-order elements and polygonal elements that have many deformational degrees of freedom. With these types of meshes, elements can deform in unphysical ways and the mesh can tangle. In this study, we present methods for obtaining more robust Lagrangian solutions on polygonal and higher-order elements. The robustness is achieved by (1) incorporating a new iterative method that modifies the velocity reconstructions in the corners of the elements, and (2) a new multidirectional approximate Riemann solver that, when coupled with the iterative method, reduces spurious mesh motion. Lastly, the details of the numerical methods are discussed and their utility is demonstrated on a diverse suite of test problems using higher-order and polygonal elements.

Authors:

^[1];

^[1]

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

Publication Date:: Tue Jun 05 00:00:00 EDT 2018

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

Sponsoring Org.:: USDOE National Nuclear Security Administration (NNSA)

OSTI Identifier:: 1477650

Alternate Identifier(s):: OSTI ID: 1548151

Report Number(s):: LA-UR-17-29885
Journal ID: ISSN 0021-9991

Grant/Contract Number:: AC52-06NA25396

Resource Type:: Accepted Manuscript

Journal Name:: Journal of Computational Physics

Additional Journal Information:: Journal Volume: 372; Journal Issue: C; Journal ID: ISSN 0021-9991

Publisher:: Elsevier

Country of Publication:: United States

Language:: English

Subject:: 97 MATHEMATICS AND COMPUTING; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Lagrangian; Cell-centered hydrodynamics; Discontinuous Galerkin; Mesh robustness; Hourglass model

Citation Formats


                    Morgan, Nathaniel Ray, Liu, Xiaodong, and Burton, Donald E. Reducing spurious mesh motion in Lagrangian finite volume and discontinuous Galerkin hydrodynamic methods.  United States: N. p., 2018. 
Web.  doi:10.1016/j.jcp.2018.06.008.

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                    Morgan, Nathaniel Ray, Liu, Xiaodong, & Burton, Donald E. Reducing spurious mesh motion in Lagrangian finite volume and discontinuous Galerkin hydrodynamic methods.  United States.  https://doi.org/10.1016/j.jcp.2018.06.008

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                    Morgan, Nathaniel Ray, Liu, Xiaodong, and Burton, Donald E. Tue .  
"Reducing spurious mesh motion in Lagrangian finite volume and discontinuous Galerkin hydrodynamic methods".  United States.  https://doi.org/10.1016/j.jcp.2018.06.008.  https://www.osti.gov/servlets/purl/1477650.

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@article{osti_1477650,

  title        = {Reducing spurious mesh motion in Lagrangian finite volume and discontinuous Galerkin hydrodynamic methods},

  author       = {Morgan, Nathaniel Ray and Liu, Xiaodong and Burton, Donald E.},

  abstractNote = {The Lagrangian finite volume (FV) cell-centered hydrodynamic (CCH) method and the Lagrangian discontinuous Galerkin (DG) CCH method have been demonstrated to be quite stable and capable of producing very accurate solutions on many mesh topologies. However, some challenges can arise with higher-order elements and polygonal elements that have many deformational degrees of freedom. With these types of meshes, elements can deform in unphysical ways and the mesh can tangle. In this study, we present methods for obtaining more robust Lagrangian solutions on polygonal and higher-order elements. The robustness is achieved by (1) incorporating a new iterative method that modifies the velocity reconstructions in the corners of the elements, and (2) a new multidirectional approximate Riemann solver that, when coupled with the iterative method, reduces spurious mesh motion. Lastly, the details of the numerical methods are discussed and their utility is demonstrated on a diverse suite of test problems using higher-order and polygonal elements.},

  doi          = {10.1016/j.jcp.2018.06.008},

  journal      = {Journal of Computational Physics},

  number       = C,

  volume       = 372,

  place        = {United States},

  year         = {Tue Jun 05 00:00:00 EDT 2018},

  month        = {Tue Jun 05 00:00:00 EDT 2018}

}

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Figure 1: The map from the initial configuration and the map from a reference element are graphically illustrated for a quadratic quadrilateral element.

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