A reconstructed discontinuous Galerkin method for multi-material hydrodynamics with sharp interfaces

Pandare, Aditya Kiran; Waltz, Jacob I.; Bakosi, Jozsef

doi:10.1002/fld.4810

Title: A reconstructed discontinuous Galerkin method for multi-material hydrodynamics with sharp interfaces

Journal Article · 13 January 2020 · International Journal for Numerical Methods in Fluids

DOI: https://doi.org/10.1002/fld.4810 · OSTI ID:1739922

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Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

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. Here, a second-order DG(P₁) method and a third-order least-squares based rDG(P₁P₂) 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.

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Research Organization:: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Sponsoring Organization:: USDOE Laboratory Directed Research and Development (LDRD) Program; USDOE National Nuclear Security Administration (NNSA)

Grant/Contract Number:: 89233218CNA000001

OSTI ID:: 1739922

Report Number(s):: LA-UR--19-20312

Journal Information:: International Journal for Numerical Methods in Fluids, Journal Name: International Journal for Numerical Methods in Fluids Journal Issue: 8 Vol. 92; ISSN 0271-2091

Publisher:: WileyCopyright Statement

Country of Publication:: United States

Language:: English

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