Reducing spurious mesh motion in Lagrangian finite volume and discontinuous Galerkin hydrodynamic methods
Abstract
The Lagrangian finite volume (FV) cellcentered 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 higherorder 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 higherorder 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 higherorder and polygonal elements.
 Authors:

 Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Publication Date:
 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):
 LAUR1729885
Journal ID: ISSN 00219991
 Grant/Contract Number:
 AC5206NA25396
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Journal of Computational Physics
 Additional Journal Information:
 Journal Volume: 372; Journal Issue: C; Journal ID: ISSN 00219991
 Publisher:
 Elsevier
 Country of Publication:
 United States
 Language:
 English
 Subject:
 97 MATHEMATICS AND COMPUTING; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Lagrangian; Cellcentered 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.
Morgan, Nathaniel Ray, Liu, Xiaodong, & Burton, Donald E. Reducing spurious mesh motion in Lagrangian finite volume and discontinuous Galerkin hydrodynamic methods. United States. doi:10.1016/j.jcp.2018.06.008.
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. doi:10.1016/j.jcp.2018.06.008. https://www.osti.gov/servlets/purl/1477650.
@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) cellcentered 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 higherorder 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 higherorder 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 higherorder and polygonal elements.},
doi = {10.1016/j.jcp.2018.06.008},
journal = {Journal of Computational Physics},
number = C,
volume = 372,
place = {United States},
year = {2018},
month = {6}
}
Web of Science