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Stability analysis of WONDY (a hydrocode based on the artificial viscosity method of von Neumann and Richtmyer) for a special case of Maxwell's law

Author: D. L. Hicks
Journal: Math. Comp. 32 (1978), 1123-1130
MSC: Primary 73.65
MathSciNet review: 0483944
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Abstract: The artificial viscosity method of von Neumann and Richtmyer was originally designed and analyzed for stability in the case when the material was an ideal gas. Recently a hydrocode (WONDY) based on the von Neumann-Richtmyer scheme was used in calculating wave propagation problems in materials obeying a form of Maxwell's material law; signs of an unstable difference scheme appeared. A stability analysis shows that the timestep restrictions required for stability in certain cases can be more stringent for material laws of the Maxwell type than they are for material laws of the ideal gas type.

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  • [1] J. ASAY, D. HICKS & D. HOLDRIDGE, "Comparison of experimental and calculated elastic-plastic wave profiles in LiF," J. Appl. Phys., v. 46, 1975, pp. 4316-4322.
  • [2] W. HERMANN, P. HOLZHAUSER & R. THOMPSON, WONDY: A Computer Program for Calculating Problems of Motion in One Dimension, Sandia Laboratories Report SC-RR-66-601, 1966.
  • [3] H. G. KOLSKY, A Method for the Numerical Solution of Transient Hydrodynamic Shock Problems in Two Space Dimensions, Los Alamos Laboratories Report LA-1867, 1954.
  • [4] Robert D. Richtmyer and K. W. Morton, Difference methods for initial-value problems, Second edition. Interscience Tracts in Pure and Applied Mathematics, No. 4, Interscience Publishers John Wiley & Sons, Inc., New York-London-Sydney, 1967. MR 0220455
  • [5] J. Von Neumann and R. D. Richtmyer, A method for the numerical calculation of hydrodynamic shocks, J. Appl. Phys. 21 (1950), 232–237. MR 0037613
  • [6] G. N. WHITE, private communication.

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Article copyright: © Copyright 1978 American Mathematical Society

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