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Numerical simulations of shock wave reflection phenomena in non-stationary flows using regularized smoothed particle hydrodynamics (RSPH)

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Abstract

In this paper we wish to demonstrate to what extent the numerical method regularized smoothed particle hydrodynamics (RSPH) is capable of modelling shocks and shock reflection patterns in a satisfactory manner. The use of SPH based methods to model shock wave problems has been relatively sparse, both due to historical reasons, as the method was originally developed for studies of astrophysical gas dynamics, but also due to the fact that boundary treatment in Lagrangian methods may be a difficult task. The boundary conditions have therefore been given special attention in this paper. Results presented for one quasi-stationary and three non-stationary flow tests reveal a high degree of similarity, when compared to published numerical and experimental data. The difference is found to be below 5, in the case where experimental data was found tabulated. The transition from regular reflection (RR) to Mach reflection (MR) and the opposite transition from MR to RR are studied. The results are found to be in close agreement with the results obtained from various empirical and semi-empirical formulas published in the literature. A convergence test shows a convergence rate slightly steeper than linear, comparable to what is found for other numerical methods when shocks are involved.

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Authors and Affiliations

  1. Norwegian Defence Estates Agency, P.O. Box 405, 0103, Oslo, Norway

    M. Omang

  2. Institute of Theoretical Astrophysics, University of Oslo, P.O. Box 1029, Blindern, 0315, Oslo, Norway

    S. Børve & J. Trulsen

Authors
  1. M. Omang
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  2. S. Børve
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  3. J. Trulsen
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Correspondence to M. Omang.

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Communicated by O. Igra.

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Omang, M., Børve, S. & Trulsen, J. Numerical simulations of shock wave reflection phenomena in non-stationary flows using regularized smoothed particle hydrodynamics (RSPH). Shock Waves 16, 167–177 (2006). https://doi.org/10.1007/s00193-006-0061-y

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