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Title: Dynamic mesh adaptation for front evolution using discontinuous Galerkin based weighted condition number relaxation

Abstract

A new mesh smoothing method designed to cluster cells near a dynamically evolving interface is presented. The method is based on weighted condition number mesh relaxation with the weight function computed from a level set representation of the interface. The weight function is expressed as a Taylor series based discontinuous Galerkin projection, which makes the computation of the derivatives of the weight function needed during the condition number optimization process a trivial matter. For cases when a level set is not available, a fast method for generating a low-order level set from discrete cell-centered fields, such as a volume fraction or index function, is provided. Results show that the low-order level set works equally well as the actual level set for mesh smoothing. Meshes generated for a number of interface geometries are presented, including cases with multiple level sets. Lastly, dynamic cases with moving interfaces show the new method is capable of maintaining a desired resolution near the interface with an acceptable number of relaxation iterations per time step, which demonstrates the method's potential to be used as a mesh relaxer for arbitrary Lagrangian Eulerian (ALE) methods.

Authors:
ORCiD logo [1];  [1];  [1]
  1. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Publication Date:
Research Org.:
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1345322
Alternate Identifier(s):
OSTI ID: 1397833
Report Number(s):
LLNL-JRNL-703859
Journal ID: ISSN 0021-9991; TRN: US1700926
Grant/Contract Number:  
AC52-07NA27344
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Journal of Computational Physics
Additional Journal Information:
Journal Volume: 335; Journal Issue: C; Journal ID: ISSN 0021-9991
Publisher:
Elsevier
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; weighted mesh smoothing; condition number mesh relaxation; r-Refinement; level set; discontinuous Galerkin discretization; ALE method; WENO

Citation Formats

Greene, Patrick T., Schofield, Samuel P., and Nourgaliev, Robert. Dynamic mesh adaptation for front evolution using discontinuous Galerkin based weighted condition number relaxation. United States: N. p., 2017. Web. doi:10.1016/j.jcp.2017.01.049.
Greene, Patrick T., Schofield, Samuel P., & Nourgaliev, Robert. Dynamic mesh adaptation for front evolution using discontinuous Galerkin based weighted condition number relaxation. United States. doi:10.1016/j.jcp.2017.01.049.
Greene, Patrick T., Schofield, Samuel P., and Nourgaliev, Robert. Fri . "Dynamic mesh adaptation for front evolution using discontinuous Galerkin based weighted condition number relaxation". United States. doi:10.1016/j.jcp.2017.01.049. https://www.osti.gov/servlets/purl/1345322.
@article{osti_1345322,
title = {Dynamic mesh adaptation for front evolution using discontinuous Galerkin based weighted condition number relaxation},
author = {Greene, Patrick T. and Schofield, Samuel P. and Nourgaliev, Robert},
abstractNote = {A new mesh smoothing method designed to cluster cells near a dynamically evolving interface is presented. The method is based on weighted condition number mesh relaxation with the weight function computed from a level set representation of the interface. The weight function is expressed as a Taylor series based discontinuous Galerkin projection, which makes the computation of the derivatives of the weight function needed during the condition number optimization process a trivial matter. For cases when a level set is not available, a fast method for generating a low-order level set from discrete cell-centered fields, such as a volume fraction or index function, is provided. Results show that the low-order level set works equally well as the actual level set for mesh smoothing. Meshes generated for a number of interface geometries are presented, including cases with multiple level sets. Lastly, dynamic cases with moving interfaces show the new method is capable of maintaining a desired resolution near the interface with an acceptable number of relaxation iterations per time step, which demonstrates the method's potential to be used as a mesh relaxer for arbitrary Lagrangian Eulerian (ALE) methods.},
doi = {10.1016/j.jcp.2017.01.049},
journal = {Journal of Computational Physics},
number = C,
volume = 335,
place = {United States},
year = {Fri Jan 27 00:00:00 EST 2017},
month = {Fri Jan 27 00:00:00 EST 2017}
}

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