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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

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
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by D. L. Hicks PDF
Math. Comp. 32 (1978), 1123-1130 Request permission

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.
References
    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. 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. 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.
  • Robert D. Richtmyer and K. W. Morton, Difference methods for initial-value problems, 2nd ed., Interscience Tracts in Pure and Applied Mathematics, No. 4, Interscience Publishers John Wiley & Sons, Inc., New York-London-Sydney, 1967. MR 0220455
  • J. Von Neumann and R. D. Richtmyer, A method for the numerical calculation of hydrodynamic shocks, J. Appl. Phys. 21 (1950), 232–237. MR 37613, DOI 10.1063/1.1699639
    • G. N. WHITE, private communication.
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Additional Information
  • © Copyright 1978 American Mathematical Society
  • Journal: Math. Comp. 32 (1978), 1123-1130
  • MSC: Primary 73.65
  • DOI: https://doi.org/10.1090/S0025-5718-1978-0483944-0
  • MathSciNet review: 0483944