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Title: Compatible, energy conserving, bounds preserving remap of hydrodynamic fields for an extended ALE scheme

Abstract

From the very origins of numerical hydrodynamics in the Lagrangian work of von Neumann and Richtmyer [83], the issue of total energy conservation as well as entropy production has been problematic. Because of well known problems with mesh deformation, Lagrangian schemes have evolved into Arbitrary Lagrangian–Eulerian (ALE) methods [39] that combine the best properties of Lagrangian and Eulerian methods. Energy issues have persisted for this class of methods. We believe that fundamental issues of energy conservation and entropy production in ALE require further examination. The context of the paper is an ALE scheme that is extended in the sense that it permits cyclic or periodic remap of data between grids of the same or differing connectivity. The principal design goals for a remap method then consist of total energy conservation, bounded internal energy, and compatibility of kinetic energy and momentum. We also have secondary objectives of limiting velocity and stress in a non-directional manner, keeping primitive variables monotone, and providing a higher than second order reconstruction of remapped variables. Particularly, the new contributions fall into three categories associated with: energy conservation and entropy production, reconstruction and bounds preservation of scalar and tensor fields, and conservative remap of nonlinear fields. Ourmore » paper presents a derivation of the methods, details of implementation, and numerical results for a number of test problems. The methods requires volume integration of polynomial functions in polytopal cells with planar facets, and the requisite expressions are derived for arbitrary order.« less

Authors:
ORCiD logo [1]; ORCiD logo [1];  [1];  [1]; ORCiD logo [1]
  1. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Publication Date:
Research Org.:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA)
OSTI Identifier:
1411348
Report Number(s):
LA-UR-17-21696
Journal ID: ISSN 0021-9991; TRN: US1800221
Grant/Contract Number:
AC52-06NA25396
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Journal of Computational Physics
Additional Journal Information:
Journal Volume: 355; Journal Issue: C; Journal ID: ISSN 0021-9991
Publisher:
Elsevier
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Lagrangian,hydrodynamics,remap,mimetic,cell-centered,ALE,exactintersection,KEfixup, finite-volume

Citation Formats

Burton, Donald E., Morgan, Nathaniel Ray, Charest, Marc Robert Joseph, Kenamond, Mark Andrew, and Fung, Jimmy. Compatible, energy conserving, bounds preserving remap of hydrodynamic fields for an extended ALE scheme. United States: N. p., 2017. Web. doi:10.1016/j.jcp.2017.11.017.
Burton, Donald E., Morgan, Nathaniel Ray, Charest, Marc Robert Joseph, Kenamond, Mark Andrew, & Fung, Jimmy. Compatible, energy conserving, bounds preserving remap of hydrodynamic fields for an extended ALE scheme. United States. doi:10.1016/j.jcp.2017.11.017.
Burton, Donald E., Morgan, Nathaniel Ray, Charest, Marc Robert Joseph, Kenamond, Mark Andrew, and Fung, Jimmy. Wed . "Compatible, energy conserving, bounds preserving remap of hydrodynamic fields for an extended ALE scheme". United States. doi:10.1016/j.jcp.2017.11.017.
@article{osti_1411348,
title = {Compatible, energy conserving, bounds preserving remap of hydrodynamic fields for an extended ALE scheme},
author = {Burton, Donald E. and Morgan, Nathaniel Ray and Charest, Marc Robert Joseph and Kenamond, Mark Andrew and Fung, Jimmy},
abstractNote = {From the very origins of numerical hydrodynamics in the Lagrangian work of von Neumann and Richtmyer [83], the issue of total energy conservation as well as entropy production has been problematic. Because of well known problems with mesh deformation, Lagrangian schemes have evolved into Arbitrary Lagrangian–Eulerian (ALE) methods [39] that combine the best properties of Lagrangian and Eulerian methods. Energy issues have persisted for this class of methods. We believe that fundamental issues of energy conservation and entropy production in ALE require further examination. The context of the paper is an ALE scheme that is extended in the sense that it permits cyclic or periodic remap of data between grids of the same or differing connectivity. The principal design goals for a remap method then consist of total energy conservation, bounded internal energy, and compatibility of kinetic energy and momentum. We also have secondary objectives of limiting velocity and stress in a non-directional manner, keeping primitive variables monotone, and providing a higher than second order reconstruction of remapped variables. Particularly, the new contributions fall into three categories associated with: energy conservation and entropy production, reconstruction and bounds preservation of scalar and tensor fields, and conservative remap of nonlinear fields. Our paper presents a derivation of the methods, details of implementation, and numerical results for a number of test problems. The methods requires volume integration of polynomial functions in polytopal cells with planar facets, and the requisite expressions are derived for arbitrary order.},
doi = {10.1016/j.jcp.2017.11.017},
journal = {Journal of Computational Physics},
number = C,
volume = 355,
place = {United States},
year = {Wed Nov 22 00:00:00 EST 2017},
month = {Wed Nov 22 00:00:00 EST 2017}
}

Journal Article:
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