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

Journal Article · · Computers and Mathematics with Applications (Oxford)
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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.

Research Organization:
Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
Sponsoring Organization:
USDOE National Nuclear Security Administration (NNSA)
Grant/Contract Number:
AC52-06NA25396; LA-UR-17-30562
OSTI ID:
1989709
Alternate ID(s):
OSTI ID: 1454997; OSTI ID: 1703670
Report Number(s):
LA-UR-17-30562; S0898122118302943; PII: S0898122118302943
Journal Information:
Computers and Mathematics with Applications (Oxford), Journal Name: Computers and Mathematics with Applications (Oxford) Vol. 78 Journal Issue: 2; ISSN 0898-1221
Publisher:
ElsevierCopyright Statement
Country of Publication:
United Kingdom
Language:
English
Citation Metrics:
Cited by: 3 works
Citation information provided by
Web of Science

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Figures / Tables (22)

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Related Subjects

97 MATHEMATICS AND COMPUTING
slope limiter
piecewise linear reconstruction
adaptively refined mesh
finite volume method
Euler equation