A reconstructed discontinuous Galerkin method for multi‐material hydrodynamics with sharp interfaces Article Swipe
Aditya Pandare
,
Jacob Waltz
,
József Bakosi
·
YOU?
·
· 2020
· Open Access
·
· DOI: https://doi.org/10.1002/fld.4810
YOU?
·
· 2020
· Open Access
·
· DOI: https://doi.org/10.1002/fld.4810
Summary Discontinuous Galerkin (DG) methods have been well established for single‐material hydrodynamics. However, consistent DG discretizations for non‐equilibrium multi‐material (more than two materials) hydrodynamics have not been extensively studied. In this work, a novel reconstructed DG (rDG) method for the single‐velocity multi‐material system is presented. The multi‐material system being considered assumes stiff velocity relaxation, but does not assume pressure and temperature equilibrium between the multiple materials. A second‐order DG(P 1 ) method and a third‐order least‐squares based rDG(P 1 P 2 ) are used to discretize this system in space, and a third‐order total variation diminishing (TVD) Runge‐Kutta method is used to integrate in time. A well‐balanced DG discretization of the non‐conservative system is presented and is verified by numerical test problems. Furthermore, a consistent interface treatment is implemented, which ensures strict conservation of material masses and total energy. Numerical tests indicate that the DG and rDG methods are, indeed, the second‐ and third‐order accurate. Comparisons with the second‐order finite volume method show that the DG and rDG methods are able to capture the interfaces more sharply. The DG and rDG methods are also more accurate in the single‐material regions of the flow. This work focuses on the general multidimensional rDG formulation of the non‐equilibrium multi‐material system and a study of properties of the method via one‐dimensional numerical experiments. The results from this research will be the foundation for a multidimensional high‐order rDG method for multi‐material hydrodynamics.
Related Topics
Concepts
Discretization
Discontinuous Galerkin method
Total variation diminishing
Applied mathematics
Work (physics)
Flow (mathematics)
Finite element method
Order of accuracy
Finite volume method
Galerkin method
Mathematical optimization
Numerical analysis
Computer science
Mathematics
Mathematical analysis
Mechanics
Physics
Geometry
Numerical stability
Thermodynamics
Metadata
- Type
- article
- Language
- en
- Landing Page
- https://doi.org/10.1002/fld.4810
- OA Status
- green
- Cited By
- 25
- References
- 53
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W2999891835
All OpenAlex metadata
Raw OpenAlex JSON
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https://openalex.org/W2999891835Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.1002/fld.4810Digital Object Identifier
- Title
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A reconstructed discontinuous Galerkin method for multi‐material hydrodynamics with sharp interfacesWork title
- Type
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articleOpenAlex work type
- Language
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enPrimary language
- Publication year
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2020Year of publication
- Publication date
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2020-01-14Full publication date if available
- Authors
-
Aditya Pandare, Jacob Waltz, József BakosiList of authors in order
- Landing page
-
https://doi.org/10.1002/fld.4810Publisher landing page
- Open access
-
YesWhether a free full text is available
- OA status
-
greenOpen access status per OpenAlex
- OA URL
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https://www.osti.gov/biblio/1595874Direct OA link when available
- Concepts
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Discretization, Discontinuous Galerkin method, Total variation diminishing, Applied mathematics, Work (physics), Flow (mathematics), Finite element method, Order of accuracy, Finite volume method, Galerkin method, Mathematical optimization, Numerical analysis, Computer science, Mathematics, Mathematical analysis, Mechanics, Physics, Geometry, Numerical stability, ThermodynamicsTop concepts (fields/topics) attached by OpenAlex
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25Total citation count in OpenAlex
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2025: 5, 2024: 2, 2023: 7, 2022: 6, 2021: 3Per-year citation counts (last 5 years)
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53Number of works referenced by this work
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10Other works algorithmically related by OpenAlex
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