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Title: A compatible, energy and symmetry preserving Lagrangian hydrodynamics algorithm in three-dimensional Cartesian geometry

Abstract

This work presents a numerical algorithm for the solution of fluid dynamics problems with moderate to high speed flow in three dimensions. Cartesian geometry is chosen owing to the fact that in this coordinate system no curvature terms are present that break the conservation law structure of the fluid equations. Written in Lagrangian form, these equations are discretized utilizing compatible, control volume differencing with a staggered-grid placement of the spatial variables. The concept of compatibility means that the forces used in the momentum equation to advance velocity are also incorporated into the internal energy equation so that these equations together define the total energy as a quantity that is exactly conserved in time in discrete form. Multiple pressures are utilized in each zone; they produce forces that resist spurious vorticity generation. This difficulty can severely limit the utility of the Lagrangian formulation in two dimensions and make this representation otherwise virtually useless in three dimensions. An edge-centered artificial viscosity whose magnitude is regulated by local velocity gradients is used to capture shocks. The particular difficulty of exactly preserving one-dimensional spherical symmetry in three-dimensional geometry is solved. This problem has both practical and pedagogical significance. The algorithm is suitable for bothmore » structured and unstructured grids. Limitations that symmetry preservation imposes on the latter type of grids are delineated.« less

Authors:
; ;
Publication Date:
Research Org.:
Los Alamos National Lab., NM (US)
OSTI Identifier:
20014345
Resource Type:
Journal Article
Journal Name:
Journal of Computational Physics
Additional Journal Information:
Journal Volume: 157; Journal Issue: 1; Other Information: PBD: 1 Jan 2000; Journal ID: ISSN 0021-9991
Country of Publication:
United States
Language:
English
Subject:
66 PHYSICS; 99 MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; ALGORITHMS; NUMERICAL SOLUTION; HYDRODYNAMICS; THREE-DIMENSIONAL CALCULATIONS; CARTESIAN COORDINATES; LAGRANGIAN FUNCTION; SHOCK WAVES; CONSERVATION LAWS

Citation Formats

Caramana, E J, Rousculp, C L, and Burton, D E. A compatible, energy and symmetry preserving Lagrangian hydrodynamics algorithm in three-dimensional Cartesian geometry. United States: N. p., 2000. Web. doi:10.1006/jcph.1999.6368.
Caramana, E J, Rousculp, C L, & Burton, D E. A compatible, energy and symmetry preserving Lagrangian hydrodynamics algorithm in three-dimensional Cartesian geometry. United States. https://doi.org/10.1006/jcph.1999.6368
Caramana, E J, Rousculp, C L, and Burton, D E. 2000. "A compatible, energy and symmetry preserving Lagrangian hydrodynamics algorithm in three-dimensional Cartesian geometry". United States. https://doi.org/10.1006/jcph.1999.6368.
@article{osti_20014345,
title = {A compatible, energy and symmetry preserving Lagrangian hydrodynamics algorithm in three-dimensional Cartesian geometry},
author = {Caramana, E J and Rousculp, C L and Burton, D E},
abstractNote = {This work presents a numerical algorithm for the solution of fluid dynamics problems with moderate to high speed flow in three dimensions. Cartesian geometry is chosen owing to the fact that in this coordinate system no curvature terms are present that break the conservation law structure of the fluid equations. Written in Lagrangian form, these equations are discretized utilizing compatible, control volume differencing with a staggered-grid placement of the spatial variables. The concept of compatibility means that the forces used in the momentum equation to advance velocity are also incorporated into the internal energy equation so that these equations together define the total energy as a quantity that is exactly conserved in time in discrete form. Multiple pressures are utilized in each zone; they produce forces that resist spurious vorticity generation. This difficulty can severely limit the utility of the Lagrangian formulation in two dimensions and make this representation otherwise virtually useless in three dimensions. An edge-centered artificial viscosity whose magnitude is regulated by local velocity gradients is used to capture shocks. The particular difficulty of exactly preserving one-dimensional spherical symmetry in three-dimensional geometry is solved. This problem has both practical and pedagogical significance. The algorithm is suitable for both structured and unstructured grids. Limitations that symmetry preservation imposes on the latter type of grids are delineated.},
doi = {10.1006/jcph.1999.6368},
url = {https://www.osti.gov/biblio/20014345}, journal = {Journal of Computational Physics},
issn = {0021-9991},
number = 1,
volume = 157,
place = {United States},
year = {Sat Jan 01 00:00:00 EST 2000},
month = {Sat Jan 01 00:00:00 EST 2000}
}