Weak boundary conditions for Lagrangian shock hydrodynamics: A high-order finite element implementation on curved boundaries

Atallah, Nabil M.; Tomov, Vladimir Z.; Scovazzi, Guglielmo

doi:10.1016/j.jcp.2024.112959

Title: Weak boundary conditions for Lagrangian shock hydrodynamics: A high-order finite element implementation on curved boundaries

Journal Article · 27 March 2024 · Journal of Computational Physics

DOI: https://doi.org/10.1016/j.jcp.2024.112959 · OSTI ID:2375411

Atallah, Nabil M. ^[1]; Tomov, Vladimir Z. ^[1]; Scovazzi, Guglielmo ^[2]

Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)
Duke Univ., Durham, NC (United States)

Here, we propose a new Nitsche-type approach for weak enforcement of normal velocity boundary conditions for a Lagrangian discretization of the compressible shock-hydrodynamics equations using high-order finite elements on curved boundaries. Specifically, the variational formulation is appropriately modified to enforce free-slip wall boundary conditions, without perturbing the structure of the function spaces used to represent the solution, with a considerable simplification with respect to traditional approaches. Total energy is conserved and the resulting mass matrices are constant in time. The robustness and accuracy of the proposed method are validated with an extensive set of tests involving nontrivial curved boundaries.

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Research Organization:: Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)

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

Grant/Contract Number:: AC52-07NA27344

OSTI ID:: 2375411

Report Number(s):: LLNL--JRNL-853773; 1081880

Journal Information:: Journal of Computational Physics, Journal Name: Journal of Computational Physics Vol. 507; ISSN 0021-9991

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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97 MATHEMATICS AND COMPUTING
Curved boundaries
High-order finite elements
Lagrangian hydrodynamics
Wall boundary conditions

Title: Weak boundary conditions for Lagrangian shock hydrodynamics: A high-order finite element implementation on curved boundaries

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