Exact conservation of energy and momentum in staggered-grid hydrodynamics with arbitrary connectivity

Conference · Fri Jun 01 04:00:00 EDT 1990

OSTI ID:6682571

Burton, D E

For general formulations of staggered-grid hydrodynamics (SGH), we show that exact difference expressions for total energy conservation are derivable directly from the difference expressions for nodal mass and momentum conservation. The results are multi-dimensional and apply to arbitrarily (as well as regularly) connected grids. In SGH the spatial centering of coordinates and velocity are at nodes while mass, internal energy, and pressure are within zones; temporally, variables are usually centered at the integer time step except for velocity which is at the half step. The momentum equation is found to lead to an exactly conserved energy flux between internal energy in the zones and kinetic energy at the nodes. Exact expressions for work, kinetic and internal energy evolution, and total energy conservation follow. The derived work expression also shows that momentum, kinetic and internal energies can be exactly defined at either full or half time steps. The energy flux is not properly calculated by those SGH methods in which the work is differenced independently of the differenced momentum equation. This leads to the community observed lack of conservation in SGH methods.

• Research Organization: Lawrence Livermore National Lab., CA (USA)
• Sponsoring Organization: DOE/DP
• DOE Contract Number: W-7405-ENG-48
• OSTI ID: 6682571
• Report Number(s): UCRL-JC-104258; CONF-9006195--5; ON: DE90015045
• Country of Publication: United States
• Language: English

Related Subjects

657002* -- Theoretical & Mathematical Physics-- Classical & Quantum Mechanics
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
CONSERVATION LAWS
ENERGY
FLUID MECHANICS
HYDRODYNAMICS
KINETIC ENERGY
LINEAR MOMENTUM
MASS
MECHANICS