Multidimensional discretization of conservation laws for unstructured polyhedral grids

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To the extent possible, a discretized system should satisfy the same conservation laws as the physical system. The author considers the conservation properties of a staggered-grid Lagrange formulation of the hydrodynamics equations (SGH) which is an extension of a ID scheme due to von Neumann and Richtmyer (VNR). The term staggered refers to spatial centering in which position, velocity, and kinetic energy are centered at nodes, while density, pressure, and internal energy are at cell centers. Traditional SGH formulations consider mass, volume, and momentum conservation, but tend to ignore conservation of total energy, conservation of angular momentum, and requirements for ... continued below

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26 p.

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Burton, D.E. August 22, 1994.

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To the extent possible, a discretized system should satisfy the same conservation laws as the physical system. The author considers the conservation properties of a staggered-grid Lagrange formulation of the hydrodynamics equations (SGH) which is an extension of a ID scheme due to von Neumann and Richtmyer (VNR). The term staggered refers to spatial centering in which position, velocity, and kinetic energy are centered at nodes, while density, pressure, and internal energy are at cell centers. Traditional SGH formulations consider mass, volume, and momentum conservation, but tend to ignore conservation of total energy, conservation of angular momentum, and requirements for thermodynamic reversibility. The author shows that, once the mass and momentum discretizations have been specified, discretization for other quantities are dictated by the conservation laws and cannot be independently defined. The spatial discretization method employs a finite volume procedure that replaces differential operators with surface integrals. The method is appropriate for multidimensional formulations (1D, 2D, 3D) on unstructured grids formed from polygonal (2D) or polyhedral (3D) cells. Conservation equations can then be expressed in conservation form in which conserved currents are exchanged between control volumes. In addition to the surface integrals, the conservation equations include source terms derived from physical sources or geometrical considerations. In Cartesian geometry, mass and momentum are conserved identically. Discussion of volume conservation will be temporarily deferred. The author shows that the momentum equation leads to a form-preserving definition for kinetic energy and to an exactly conservative evolution equation for internal energy. Similarly, the author derives a form-preserving definition and corresponding conservation equation for a zone-centered angular momentum.

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26 p.

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OSTI as DE95008796

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  • SAMGOP-94: 2nd international workshop on analytical methods and process optimization in fluid and gas mechanics, Arzamas (Russian Federation), 10-16 Sep 1994

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  • Other: DE95008796
  • Report No.: UCRL-JC--118306
  • Report No.: CONF-9409314--1
  • Grant Number: W-7405-ENG-48
  • Office of Scientific & Technical Information Report Number: 35336
  • Archival Resource Key: ark:/67531/metadc679957

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  • August 22, 1994

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  • July 25, 2015, 2:20 a.m.

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  • Feb. 23, 2016, 2:05 p.m.

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Burton, D.E. Multidimensional discretization of conservation laws for unstructured polyhedral grids, article, August 22, 1994; California. (digital.library.unt.edu/ark:/67531/metadc679957/: accessed January 17, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.