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Title: Direction-aware slope limiter for three-dimensional cubic grids with adaptive mesh refinement

Abstract

In the context of finite volume methods for hyperbolic systems of conservation laws, slope limiters are an effective way to suppress creation of unphysical local extrema and/or oscillations near discontinuities. We investigate properties of these limiters as applied to piecewise linear reconstructions of conservative fluid quantities in three-dimensional simulations. In particular, we are interested in linear reconstructions on Cartesian adaptively refined meshes, where a reconstructed fluid quantity at a face center depends on more than a single gradient component of the quantity. We design a new slope limiter, which combines the robustness of a minmod limiter with the accuracy of a van Leer limiter. The limiter is called Direction-Aware Limiter (DAL), because the combination is based on a principal flow direction. In particular, DAL is useful in situations where the Barth–Jespersen limiter for general meshes fails to maintain global linear functions, such as on cubic computational meshes with stencils including only faceneighboring cells. Here, we verify the new slope limiter on a suite of standard hydrodynamic test problems on Cartesian adaptively refined meshes. Lastly, we demonstrate reduced mesh imprinting; for radially symmetric problems such as the Sedov blast wave or the Noh implosion test cases, the results with DAL showmore » better preservation of radial symmetry compared to the other standard methods on Cartesian meshes.« less

Authors:
; ;
Publication Date:
Research Org.:
Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA)
OSTI Identifier:
1989709
Alternate Identifier(s):
OSTI ID: 1454997; OSTI ID: 1703670
Report Number(s):
LA-UR-17-30562
Journal ID: ISSN 0898-1221; S0898122118302943; PII: S0898122118302943
Grant/Contract Number:  
AC52-06NA25396; LA-UR-17-30562
Resource Type:
Published Article
Journal Name:
Computers and Mathematics with Applications (Oxford)
Additional Journal Information:
Journal Name: Computers and Mathematics with Applications (Oxford) Journal Volume: 78 Journal Issue: 2; Journal ID: ISSN 0898-1221
Publisher:
Elsevier
Country of Publication:
United Kingdom
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; slope limiter; piecewise linear reconstruction; adaptively refined mesh; finite volume method; Euler equation

Citation Formats

Velechovsky, Jan, Francois, Marianne, and Masser, Thomas. Direction-aware slope limiter for three-dimensional cubic grids with adaptive mesh refinement. United Kingdom: N. p., 2019. Web. doi:10.1016/j.camwa.2018.05.026.
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Velechovsky, Jan, Francois, Marianne, & Masser, Thomas. Direction-aware slope limiter for three-dimensional cubic grids with adaptive mesh refinement. United Kingdom. https://doi.org/10.1016/j.camwa.2018.05.026
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Velechovsky, Jan, Francois, Marianne, and Masser, Thomas. Mon . "Direction-aware slope limiter for three-dimensional cubic grids with adaptive mesh refinement". United Kingdom. https://doi.org/10.1016/j.camwa.2018.05.026.
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@article{osti_1989709,
title = {Direction-aware slope limiter for three-dimensional cubic grids with adaptive mesh refinement},
author = {Velechovsky, Jan and Francois, Marianne and Masser, Thomas},
abstractNote = {In the context of finite volume methods for hyperbolic systems of conservation laws, slope limiters are an effective way to suppress creation of unphysical local extrema and/or oscillations near discontinuities. We investigate properties of these limiters as applied to piecewise linear reconstructions of conservative fluid quantities in three-dimensional simulations. In particular, we are interested in linear reconstructions on Cartesian adaptively refined meshes, where a reconstructed fluid quantity at a face center depends on more than a single gradient component of the quantity. We design a new slope limiter, which combines the robustness of a minmod limiter with the accuracy of a van Leer limiter. The limiter is called Direction-Aware Limiter (DAL), because the combination is based on a principal flow direction. In particular, DAL is useful in situations where the Barth–Jespersen limiter for general meshes fails to maintain global linear functions, such as on cubic computational meshes with stencils including only faceneighboring cells. Here, we verify the new slope limiter on a suite of standard hydrodynamic test problems on Cartesian adaptively refined meshes. Lastly, we demonstrate reduced mesh imprinting; for radially symmetric problems such as the Sedov blast wave or the Noh implosion test cases, the results with DAL show better preservation of radial symmetry compared to the other standard methods on Cartesian meshes.},
doi = {10.1016/j.camwa.2018.05.026},
journal = {Computers and Mathematics with Applications (Oxford)},
number = 2,
volume = 78,
place = {United Kingdom},
year = {Mon Jul 01 00:00:00 EDT 2019},
month = {Mon Jul 01 00:00:00 EDT 2019}
}
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Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
https://doi.org/10.1016/j.camwa.2018.05.026
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Cited by: 3 works
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Figures / Tables:

Fig. 1 Fig. 1: Sweby region (hatch) and the generalized van Leer limiter (green) for $α$ ∈ (1, 2). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
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    Figures / Tables found in this record:

    Fig. 1 (p. 5)figure
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