Numerical anomalies mimicking physical effects

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Numerical simulations of flows with shock waves typically use finite-difference shock-capturing algorithms. These algorithms give a shock a numerical width in order to generate the entropy increase that must occur across a shock wave. For algorithms in conservation form, steady-state shock waves are insensitive to the numerical dissipation because of the Hugoniot jump conditions. However, localized numerical errors occur when shock waves interact. Examples are the ``excess wall heating`` in the Noh problem (shock reflected from rigid wall), errors when a shock impacts a material interface or an abrupt change in mesh spacing, and the start-up error from initializing a ... continued below

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8 p.

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Menikoff, R. September 1, 1995.

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Numerical simulations of flows with shock waves typically use finite-difference shock-capturing algorithms. These algorithms give a shock a numerical width in order to generate the entropy increase that must occur across a shock wave. For algorithms in conservation form, steady-state shock waves are insensitive to the numerical dissipation because of the Hugoniot jump conditions. However, localized numerical errors occur when shock waves interact. Examples are the ``excess wall heating`` in the Noh problem (shock reflected from rigid wall), errors when a shock impacts a material interface or an abrupt change in mesh spacing, and the start-up error from initializing a shock as a discontinuity. This class of anomalies can be explained by the entropy generation that occurs in the transient flow when a shock profile is formed or changed. The entropy error is localized spatially but under mesh refinement does not decrease in magnitude. Similar effects have been observed in shock tube experiments with partly dispersed shock waves. In this case, the shock has a physical width due to a relaxation process. An entropy anomaly from a transient shock interaction is inherent in the structure of the conservation equations for fluid flow. The anomaly can be expected to occur whenever heat conduction can be neglected and a shock wave has a non-zero width, whether the width is physical or numerical. Thus, the numerical anomaly from an artificial shock width mimics a real physical effect.

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8 p.

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OSTI as DE95016984

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  • American Physical Society biennial conference on shock compression of condensed matter, Seattle, WA (United States), 13-18 Aug 1995

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  • Other: DE95016984
  • Report No.: LA-UR--95-2628
  • Report No.: CONF-950846--9
  • Grant Number: W-7405-ENG-36
  • Office of Scientific & Technical Information Report Number: 105651
  • Archival Resource Key: ark:/67531/metadc618760

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  • September 1, 1995

Added to The UNT Digital Library

  • June 16, 2015, 7:43 a.m.

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  • Feb. 25, 2016, 10:06 p.m.

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Menikoff, R. Numerical anomalies mimicking physical effects, article, September 1, 1995; New Mexico. (digital.library.unt.edu/ark:/67531/metadc618760/: accessed July 23, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.