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Errors for calculations of strong shocks using an artificial viscosity and an artificial heat flux.(English)Zbl 0619.76091

The artificial viscosity (Q) method of von Neumann and Richtmyer is a tremendously useful numerical technique for following shocks wherever and whenever they appear in the flow. We show that it must be used with some caution, however, as serious Q-induced errors (on the order of 100 %) can occur in some strong shock calculations. We investigate three types of Q errors: 1. Excess Q heating, of which there are two types: (a) excess wall heating on shock formation and (b) shockless Q heating; 2. Q errors when shocks are propagated over a nonuniform mesh; and 3. Q errors in propagating shocks in spherical geometry.

MSC:

76L05 Shock waves and blast waves in fluid mechanics
76M99 Basic methods in fluid mechanics
80A20 Heat and mass transfer, heat flow (MSC2010)
65Z05 Applications to the sciences

Cite

References:

[1]Von Neumann, J.; Richtmyer, R. D., J. Appl. Phys., 21, 232 (1950) ·Zbl 0037.12002
[2]Noh, W. F., UCRL-89623 (1983), Lawrence Livermore National Laboratory: Lawrence Livermore National Laboratory Livermore, CA, (unpublished)
[3]Richtmyer, R. D.; Morton, K. W., Interscience Tracts in Pure and Applied Mathematics, ((1967), Interscience: Interscience New York)
[4]Trulio, J. F.; Trigger, K. R., UCRL-6267 (1961), Lawrence Livermore National Laboratory: Lawrence Livermore National Laboratory Livermore, CA, (unpublished)
[5]Noh, W. F., UCRL-7463 (1963), Lawrence Livermore National Laboratory: Lawrence Livermore National Laboratory Livermore, CA, (unpublished)
[6]White, J., J. Comput. Phys., 12, 553 (1973)
[7]Colella, P.; Woodward, P., LBL-14661 (1982), Lawrence Berkeley Laboratory: Lawrence Berkeley Laboratory Berkeley, CA, (unpublished)
[8]Schulz, W. D., J. Math. Phys., 5, 133 (1964) ·Zbl 0208.53703
[9]P. P. Whalen;P. P. Whalen
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
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