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A MUSCL-SCNI approach for meshfree modeling of shock waves in fluids

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Abstract

A stable and nodally integrated meshfree formulation for modeling shock waves in fluids is developed. The reproducing kernel approximation is employed to discretize the conservation equations for compressible flow, and a flux vector splitting approach is applied to allow proper numerical treatments for the advection and pressure parts, respectively, based on the characteristics of each flux term. To capture the essential shock physics in fluids, including the Rankine–Hugoniot jump conditions and the entropy condition, local Riemann enrichment is introduced under the stabilized conforming nodal integration (SCNI) framework. Meanwhile, numerical instabilities associated with the advection flux are eliminated by adopting a modified upwind scheme. To further enhance accuracy, a MUSCL-type method is introduced in conjunction with an oscillation limiter to avoid Gibbs phenomenon and ensure monotonic piecewise linear reconstruction in the smooth region. The present meshfree formulation is free from tunable artificial parameters and is capable of capturing shock and rarefaction waves without over/undershoots. Several numerical examples are analyzed to demonstrate the effectiveness of the proposed MUSCL-SCNI approach in meshfree modeling of complex shock phenomena, including shock diffraction, shock–vortex interaction, and high energy explosion processes.

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Acknowledgements

The support from US Army Engineer Research and Development Center under the contract PLA-0009 and the support from Sandia National Laboratories under the contract 1655264 to the University of California, San Diego, are greatly appreciated. Permission to publish was granted by Director, Geotechnical and Structures Laboratory of the US Army Engineer Research and Development Center. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology and Engineering Solutions of Sandia LLC, a wholly owned subsidiary of Honeywell International Inc. for the US Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525.

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Authors and Affiliations

  1. Department of Structural Engineering, University of California, San Diego, La Jolla, CA, USA

    Tsung-Hui Huang, Jiun-Shyan Chen & Haoyan Wei

  2. U.S. Army Engineer Research and Development Center, Vicksburg, MS, USA

    Michael J. Roth & Jesse A. Sherburn

  3. Sandia National Laboratories, Albuquerque, NM, USA

    Joseph E. Bishop, Michael R. Tupek & Eliot H. Fang

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  1. Tsung-Hui Huang
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Huang, TH., Chen, JS., Wei, H. et al. A MUSCL-SCNI approach for meshfree modeling of shock waves in fluids. Comp. Part. Mech. 7, 329–350 (2020). https://doi.org/10.1007/s40571-019-00248-x

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