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High Order Finite Difference Methods with Subcell Resolution for Stiff Multispecies Discontinuity Capturing

Published online by Cambridge University Press:  22 January 2015

Wei Wang ,
Chi-Wang Shu ,
H.C. Yee ,
Dmitry V. Kotov  and
Björn Sjögreen
Wei Wang*
Affiliation:
Department of Mathematics and Statistics, Florida International University, Miami, FL 33199, USA
Chi-Wang Shu
Affiliation:
Division of Applied Mathematics, Brown University, Providence, RI 02912, USA
H.C. Yee
Affiliation:
NASA Ames Research Center, Moffett Field, CA 94035, USA
Dmitry V. Kotov
Affiliation:
Bay Area Environmental Research Institute, 625 2nd St. Ste 209 Petaluma, CA 94952, USA
Björn Sjögreen
Affiliation:
Lawrence Livermore National Laboratory, Livermore, CA 94551, USA
*
*Email addresses: weiwang1@fiu.edu (W. Wang), shu@dam.brown.edu (C.-W. Shu), helen.m.yee@nasa.gov (H. C. Yee), dmitry.v.kotov@nasa.gov (D. V. Kotov), sjogreen2@llnl.gov (B. Sjögreen)
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Abstract

In this paper, we extend the high order finite-difference method with subcell resolution (SR) in [34] for two-species stiff one-reaction models to multispecies and multireaction inviscid chemical reactive flows, which are significantly more difficult because of the multiple scales generated by different reactions. For reaction problems, when the reaction time scale is very small, the reaction zone scale is also small and the governing equations become very stiff. Wrong propagation speed of discontinuity may occur due to the underresolved numerical solution in both space and time. The present SR method for reactive Euler system is a fractional step method. In the convection step, any high order shock-capturing method can be used. In the reaction step, an ODE solver is applied but with certain computed flow variables in the shock region modified by the Harten subcell resolution idea. Several numerical examples of multispecies and multireaction reactive flows are performed in both one and two dimensions. Studies demonstrate that the SR method can capture the correct propagation speed of discontinuities in very coarse meshes.

Keywords

65M0676V0580A32Stiff reaction termshock capturingdetonationWENOENO subcell resolutionmultispeciesmultireactions
Type
Research Article
Information
Communications in Computational Physics , Volume 17 , Issue 2 , February 2015 , pp. 317 - 336
Copyright
Copyright © Global Science Press Limited 2015 

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