High-Order Multi-Material ALE Hydrodynamics

Anderson, Robert W.; Dobrev, Veselin A.; Kolev, Tzanio V.; Rieben, Robert N.; Tomov, Vladimir Z.

doi:10.1137/17M1116453

Title: High-Order Multi-Material ALE Hydrodynamics

Abstract

Here, we present a new approach for multi-material arbitrary Lagrangian--Eulerian (ALE) hydrodynamics simulations based on high-order finite elements posed on high-order 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 low-order FCT solutions, definition of conservative FCT fluxes based on primal field bounds, and monotone transitions between primal and conservative fields.

Authors:

Anderson, Robert W. ^[1]; Dobrev, Veselin A. ^[1]; Kolev, Tzanio V. ^[1]; Rieben, Robert N. ^[1]; Tomov, Vladimir Z. ^[1]

Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

Publication Date:: Thu Jan 11 00:00:00 EST 2018

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):: LLNL-JRNL-706339
Journal ID: ISSN 1064-8275; 841424

Grant/Contract Number:: AC52-07NA27344

Resource Type:: Accepted Manuscript

Journal Name:: SIAM Journal on Scientific Computing

Additional Journal Information:: Journal Volume: 40; Journal Issue: 1; Journal ID: ISSN 1064-8275

Publisher:: SIAM

Country of Publication:: United States

Language:: English

Subject:: 97 MATHEMATICS AND COMPUTING; hydrodynamics; ALE methods; multi-material flow; finite elements; curvilinear meshes; high-order methods

Citation Formats


                    Anderson, Robert W., Dobrev, Veselin A., Kolev, Tzanio V., Rieben, Robert N., and Tomov, Vladimir Z. High-Order Multi-Material ALE Hydrodynamics.  United States: N. p., 2018. 
Web.  doi:10.1137/17M1116453.

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                    Anderson, Robert W., Dobrev, Veselin A., Kolev, Tzanio V., Rieben, Robert N., & Tomov, Vladimir Z. High-Order Multi-Material ALE Hydrodynamics.  United States.  https://doi.org/10.1137/17M1116453

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                    Anderson, Robert W., Dobrev, Veselin A., Kolev, Tzanio V., Rieben, Robert N., and Tomov, Vladimir Z. Thu .  
"High-Order Multi-Material ALE Hydrodynamics".  United States.  https://doi.org/10.1137/17M1116453.  https://www.osti.gov/servlets/purl/1474269.

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@article{osti_1474269,

  title        = {High-Order Multi-Material 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 multi-material arbitrary Lagrangian--Eulerian (ALE) hydrodynamics simulations based on high-order finite elements posed on high-order 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 low-order 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         = {Thu Jan 11 00:00:00 EST 2018},

  month        = {Thu Jan 11 00:00:00 EST 2018}

}

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Figures / Tables:

Fig. 1.1: Overview of the Lagrangian and Remesh/Remap phases of the high-order ALE framework, characterized by curvilinear mesh motion and sub-zonal field resolution in both phases.

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