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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}
}

Journal Article:
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  • A new mesh smoothing method designed to cluster mesh cells near a dynamically evolving interface is presented. The method is based on weighted condition number mesh relaxation with the weight function being 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 elds, such as amore » volume fraction or index function, is provided. Results show that the low-order level set works equally well for the weight function as the actual level set. Meshes generated for a number of interface geometries are presented, including cases with multiple level sets. Dynamic cases for moving interfaces are presented to demonstrate the method's potential usefulness to arbitrary Lagrangian Eulerian (ALE) methods.« less
  • This paper presents the development of parallel direct Vlasov solvers with discontinuous Galerkin (DG) method for beam and plasma simulations in four dimensions. Both physical and velocity spaces are in two dimesions (2P2V) with unstructured mesh. Contrary to the standard particle-in-cell (PIC) approach for kinetic space plasma simulations, i.e., solving Vlasov-Maxwell equations, direct method has been used in this paper. There are several benefits to solving a Vlasov equation directly, such as avoiding noise associated with a finite number of particles and the capability to capture fine structure in the plasma. The most challanging part of a direct Vlasov solvermore » comes from higher dimensions, as the computational cost increases as N{sup 2d}, where d is the dimension of the physical space. Recently, due to the fast development of supercomputers, the possibility has become more realistic. Many efforts have been made to solve Vlasov equations in low dimensions before; now more interest has focused on higher dimensions. Different numerical methods have been tried so far, such as the finite difference method, Fourier Spectral method, finite volume method, and spectral element method. This paper is based on our previous efforts to use the DG method. The DG method has been proven to be very successful in solving Maxwell equations, and this paper is our first effort in applying the DG method to Vlasov equations. DG has shown several advantages, such as local mass matrix, strong stability, and easy parallelization. These are particularly suitable for Vlasov equations. Domain decomposition in high dimensions has been used for parallelization; these include a highly scalable parallel two-dimensional Poisson solver. Benchmark results have been shown and simulation results will be reported.« less