HighOrder MultiMaterial ALE Hydrodynamics
Abstract
Here, we present a new approach for multimaterial arbitrary LagrangianEulerian (ALE) hydrodynamics simulations based on highorder finite elements posed on highorder curvilinear meshes. The method builds on and extends our previous work in the Lagrangian and remap phases of ALE, and depends critically on a functional perspective that enables subzonal physics and material modeling. Curvilinear mesh relaxation is based on node movement, which is determined through the solution of an elliptic equation. The remap phase is posed in terms of advecting state variables between two meshes over a fictitious time interval. The resulting advection equation is solved by a discontinuous Galerkin (DG) formulation, combined with a customized Flux Corrected Transport (FCT) type algorithm. Because conservative fields are remapped, additional synchronization steps are introduced to preserve bounds with respect to primal fields. These steps include modification of the loworder FCT solutions, definition of conservative FCT fluxes based on primal field bounds, and monotone transitions between primal and conservative fields.
 Authors:

 Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
 Publication Date:
 Research Org.:
 Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
 Sponsoring Org.:
 USDOE National Nuclear Security Administration (NNSA)
 OSTI Identifier:
 1474269
 Report Number(s):
 LLNLJRNL706339
Journal ID: ISSN 10648275; 841424
 Grant/Contract Number:
 AC5207NA27344
 Resource Type:
 Accepted Manuscript
 Journal Name:
 SIAM Journal on Scientific Computing
 Additional Journal Information:
 Journal Volume: 40; Journal Issue: 1; Journal ID: ISSN 10648275
 Publisher:
 SIAM
 Country of Publication:
 United States
 Language:
 English
 Subject:
 97 MATHEMATICS AND COMPUTING; hydrodynamics; ALE methods; multimaterial flow; finite elements; curvilinear meshes; highorder methods
Citation Formats
Anderson, Robert W., Dobrev, Veselin A., Kolev, Tzanio V., Rieben, Robert N., and Tomov, Vladimir Z. HighOrder MultiMaterial ALE Hydrodynamics. United States: N. p., 2018.
Web. doi:10.1137/17M1116453.
Anderson, Robert W., Dobrev, Veselin A., Kolev, Tzanio V., Rieben, Robert N., & Tomov, Vladimir Z. HighOrder MultiMaterial ALE Hydrodynamics. United States. doi:10.1137/17M1116453.
Anderson, Robert W., Dobrev, Veselin A., Kolev, Tzanio V., Rieben, Robert N., and Tomov, Vladimir Z. Thu .
"HighOrder MultiMaterial ALE Hydrodynamics". United States. doi:10.1137/17M1116453. https://www.osti.gov/servlets/purl/1474269.
@article{osti_1474269,
title = {HighOrder MultiMaterial ALE Hydrodynamics},
author = {Anderson, Robert W. and Dobrev, Veselin A. and Kolev, Tzanio V. and Rieben, Robert N. and Tomov, Vladimir Z.},
abstractNote = {Here, we present a new approach for multimaterial arbitrary LagrangianEulerian (ALE) hydrodynamics simulations based on highorder finite elements posed on highorder curvilinear meshes. The method builds on and extends our previous work in the Lagrangian and remap phases of ALE, and depends critically on a functional perspective that enables subzonal physics and material modeling. Curvilinear mesh relaxation is based on node movement, which is determined through the solution of an elliptic equation. The remap phase is posed in terms of advecting state variables between two meshes over a fictitious time interval. The resulting advection equation is solved by a discontinuous Galerkin (DG) formulation, combined with a customized Flux Corrected Transport (FCT) type algorithm. Because conservative fields are remapped, additional synchronization steps are introduced to preserve bounds with respect to primal fields. These steps include modification of the loworder FCT solutions, definition of conservative FCT fluxes based on primal field bounds, and monotone transitions between primal and conservative fields.},
doi = {10.1137/17M1116453},
journal = {SIAM Journal on Scientific Computing},
number = 1,
volume = 40,
place = {United States},
year = {2018},
month = {1}
}
Web of Science