A High-Resolution Godunov Method for Compressible Multi-Material Flow on Overlapping Grids

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A numerical method is described for inviscid, compressible, multi-material flow in two space dimensions. The flow is governed by the multi-material Euler equations with a general mixture equation of state. Composite overlapping grids are used to handle complex flow geometry and block-structured adaptive mesh refinement (AMR) is used to locally increase grid resolution near shocks and material interfaces. The discretization of the governing equations is based on a high-resolution Godunov method, but includes an energy correction designed to suppress numerical errors that develop near a material interface for standard, conservative shock-capturing schemes. The energy correction is constructed based on a ... continued below

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Banks, J W; Schwendeman, D W; Kapila, A K & Henshaw, W D February 13, 2006.

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A numerical method is described for inviscid, compressible, multi-material flow in two space dimensions. The flow is governed by the multi-material Euler equations with a general mixture equation of state. Composite overlapping grids are used to handle complex flow geometry and block-structured adaptive mesh refinement (AMR) is used to locally increase grid resolution near shocks and material interfaces. The discretization of the governing equations is based on a high-resolution Godunov method, but includes an energy correction designed to suppress numerical errors that develop near a material interface for standard, conservative shock-capturing schemes. The energy correction is constructed based on a uniform pressure-velocity flow and is significant only near the captured interface. A variety of two-material flows are presented to verify the accuracy of the numerical approach and to illustrate its use. These flows assume an equation of state for the mixture based on Jones-Wilkins-Lee (JWL) forms for the components. This equation of state includes a mixture of ideal gases as a special case. Flow problems considered include unsteady one-dimensional shock-interface collision, steady interaction of an planar interface and an oblique shock, planar shock interaction with a collection of gas-filled cylindrical inhomogeneities, and the impulsive motion of the two-component mixture in a rigid cylindrical vessel.

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PDF-file: 45 pages; size: 4.7 Mbytes

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  • Journal Name: Journal of Computational Physics, vol. 223, N/A, April 1, 2007, pp. 262-297; Journal Volume: 223

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  • Report No.: UCRL-JRNL-219484
  • Grant Number: W-7405-ENG-48
  • Office of Scientific & Technical Information Report Number: 936486
  • Archival Resource Key: ark:/67531/metadc902321

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  • February 13, 2006

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  • Sept. 27, 2016, 1:39 a.m.

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  • Nov. 29, 2016, 12:41 p.m.

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Banks, J W; Schwendeman, D W; Kapila, A K & Henshaw, W D. A High-Resolution Godunov Method for Compressible Multi-Material Flow on Overlapping Grids, article, February 13, 2006; Livermore, California. (digital.library.unt.edu/ark:/67531/metadc902321/: accessed September 21, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.