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Title: Algebraic limitations on two-dimensional hydrodynamics simulations

Abstract

Algebraic limitations imposed by the use of connected straightline segments to define meshes for hydrodynamics simulations in two-dimensional cylindrical geometries are shown. It is shown that in the simplest smooth isentropic flow of the spherical expansion of a gas with point symmetry, commonly, and currently, used finite difference, finite volume, or finite element staggered grid hydrodynamics equations cannot simultaneously preserve energy, entropy, and sphericity on an equal-angle R - {Theta} mesh. It is further shown why finite difference codes tend to preserve sphericity and entropy, while finite element codes tend to preserve sphericity and energy. Exact difference representations of interface (cell face) pressures and work terms and of the elements of the strain rate tensor in a cell are shown. 16 refs., 5 figs.

Authors:
 [1]
  1. Los Alamos National Lab., NM (United States)
Publication Date:
OSTI Identifier:
274223
DOE Contract Number:  
W-7405-ENG-36
Resource Type:
Journal Article
Journal Name:
Journal of Computational Physics
Additional Journal Information:
Journal Volume: 124; Journal Issue: 1; Other Information: PBD: 1 Mar 1996
Country of Publication:
United States
Language:
English
Subject:
42 ENGINEERING NOT INCLUDED IN OTHER CATEGORIES; 66 PHYSICS; 99 MATHEMATICS, COMPUTERS, INFORMATION SCIENCE, MANAGEMENT, LAW, MISCELLANEOUS; GAS FLOW; MESH GENERATION; HYDRODYNAMICS; TWO-DIMENSIONAL CALCULATIONS

Citation Formats

Whalen, P P. Algebraic limitations on two-dimensional hydrodynamics simulations. United States: N. p., 1996. Web. doi:10.1006/jcph.1996.0043.
Whalen, P P. Algebraic limitations on two-dimensional hydrodynamics simulations. United States. https://doi.org/10.1006/jcph.1996.0043
Whalen, P P. 1996. "Algebraic limitations on two-dimensional hydrodynamics simulations". United States. https://doi.org/10.1006/jcph.1996.0043.
@article{osti_274223,
title = {Algebraic limitations on two-dimensional hydrodynamics simulations},
author = {Whalen, P P},
abstractNote = {Algebraic limitations imposed by the use of connected straightline segments to define meshes for hydrodynamics simulations in two-dimensional cylindrical geometries are shown. It is shown that in the simplest smooth isentropic flow of the spherical expansion of a gas with point symmetry, commonly, and currently, used finite difference, finite volume, or finite element staggered grid hydrodynamics equations cannot simultaneously preserve energy, entropy, and sphericity on an equal-angle R - {Theta} mesh. It is further shown why finite difference codes tend to preserve sphericity and entropy, while finite element codes tend to preserve sphericity and energy. Exact difference representations of interface (cell face) pressures and work terms and of the elements of the strain rate tensor in a cell are shown. 16 refs., 5 figs.},
doi = {10.1006/jcph.1996.0043},
url = {https://www.osti.gov/biblio/274223}, journal = {Journal of Computational Physics},
number = 1,
volume = 124,
place = {United States},
year = {Fri Mar 01 00:00:00 EST 1996},
month = {Fri Mar 01 00:00:00 EST 1996}
}