Multidimensional discretization of conservation laws for unstructured polyhedral grids

Conference · Mon Aug 22 04:00:00 EDT 1994

OSTI ID:35336

Burton, D E

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.

• Research Organization: Lawrence Livermore National Lab., CA (United States)
• Sponsoring Organization: USDOE, Washington, DC (United States)
• DOE Contract Number: W-7405-ENG-48
• OSTI ID: 35336
• Report Number(s): UCRL-JC--118306; CONF-9409314--1; ON: DE95008796
• Country of Publication: United States
• Language: English

Related Subjects

42 ENGINEERING
99 GENERAL AND MISCELLANEOUS
ANGULAR MOMENTUM
CALCULATION METHODS
CONSERVATION LAWS
ENERGY
HYDRODYNAMICS
MASS
MESH GENERATION