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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.98.

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Hydrocode subcycling stability
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by D. L. Hicks PDF
Math. Comp. 37 (1981), 69-78 Request permission

Abstract:

The method of artificial viscosity was originally designed by von Neumann and Richtmyer for calculating the propagation of waves in materials that were hydrodynamic and rate-independent (e.g., ideal gas law). However, hydrocodes (such as WONDY) based on this method continue to expand their repertoire of material laws even unto material laws that are rate-dependent (e.g., Maxwell’s material law). Restrictions on the timestep required for stability with material laws that are rate-dependent can be considerably more severe than restrictions of the Courant-Friedrichs-Lewy (CFL) type that are imposed in these hydrocodes. These very small timesteps can make computations very expensive. An alternative is to go ahead and integrate the conservation laws with the usual CFL timestep while subcycling (integrating with a smaller timestep) the integration of the stress-rate equation. If the subcycling is done with a large enough number of subcycles (i.e., with a small enough subcycle timestep), then the calculation is stable. Specifically, the number of subcycles must be one greater than the ratio of the CFL timestep to the relaxation time of the material.
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Additional Information
  • © Copyright 1981 American Mathematical Society
  • Journal: Math. Comp. 37 (1981), 69-78
  • MSC: Primary 65M10; Secondary 76-04, 76-08
  • DOI: https://doi.org/10.1090/S0025-5718-1981-0616360-9
  • MathSciNet review: 616360