Von Neumann stability of the WONDY wavecode for thermodynamic equations of state

Technical Report · Mon Oct 31 23:00:00 EST 1977

DOI:https://doi.org/10.2172/5299156· OSTI ID:5299156

Hicks, D. L.

Previous analyses of the von Neumann stability of the WONDY wavecode (based on the von Neumann--Richtmyer artificial viscosity method) assumed a mechanical stress--strain relation; i.e., they assumed the stress, p, to depend only on the mass density, rho. In a thermodynamic equation of state p is allowed to depend also on the specific entropy, S (or on the specific internal energy, epsilon). If p does not depend on epsilon (or S), then the Grueneisen parameter, GAMMA, is zero. Herein a von Neumann stability analysis of WONDY is done for the more general case when GAMMA is not equal to 0. The result of this analysis is the requirement that the timestep be less than the product of the material increment and a certain function f of the acoustic impedance (a); artificial viscosity coefficient, ..lambda..; and GAMMA. In a region of compression, if ..lambda.. GAMMA is greater than 0, then f(a,..lambda..,GAMMA) is smaller than f(a,..lambda..,0). Therefore, the more general stability analysis yields the result that the timestep restriction now in WONDY may be insufficient for stability in certain regions of certain calculations.

• Research Organization: Sandia Labs., Albuquerque, NM (USA)
• DOE Contract Number: EY-76-C-04-0789
• OSTI ID: 5299156
• Report Number(s): SAND-77-0934
• Country of Publication: United States
• Language: English

Related Subjects

640410* -- Fluid Physics-- General Fluid Dynamics
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
COMPUTER CODES
ENERGY
ENTROPY
EQUATIONS
EQUATIONS OF STATE
FLUID MECHANICS
HYDRODYNAMICS
MECHANICS
ONE-DIMENSIONAL CALCULATIONS
PHYSICAL PROPERTIES
RELIABILITY
SHOCK WAVES
STABILITY
STRESSES
THERMODYNAMIC PROPERTIES
THERMODYNAMICS
W CODES