Stable and flux-conserved meshfree formulation to model shocks

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• 作者：Michael J. Roth ; Jiun-Shyan Chen ; Thomas R. Slawson…
• 关键词：Meshfree ; Shock ; Gibbs phenomenon ; Riemann ; enriched stabilized conforming nodal integration ; Smoothed flux divergence
• 刊名：Computational Mechanics
• 出版年：2016
• 出版时间：May 2016
• 年：2016
• 卷：57
• 期：5
• 页码：773-792
• 全文大小：5,258 KB
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• 作者单位：Michael J. Roth (1)
  Jiun-Shyan Chen (2)
  Thomas R. Slawson (1)
  Kent T. Danielson (1)
  
  1. U.S. Army Engineer Research and Development Center, Vicksburg, MS, USA
  2. Department of Structural Engineering, University of California San Diego, San Diego, CA, USA
  
• 刊物类别：Engineering
• 刊物主题：Theoretical and Applied Mechanics
  Numerical and Computational Methods in Engineering
  Computational Science and Engineering
  Mechanics, Fluids and Thermodynamics
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1432-0924

文摘

Accurate shock modeling requires that two critical issues be addressed: (1) correct representation of the essential shock physics, and (2) control of Gibbs phenomenon oscillation at the discontinuity. In this work a stable (oscillation limiting) and flux-conserved formulation under the reproducing kernel particle method is developed for shock modeling. A smoothed flux divergence is constructed under the framework of stabilized conforming nodal integration, which is locally-enriched with a Riemann solution to satisfy the entropy production constraints. This Riemann-enriched flux divergence is embedded into the reproducing kernel formulation through a velocity correction that also provides oscillation control at the shock. The correction is constrained to the shock region by an automatic shock detection algorithm that is constructed using the intrinsic spectral decomposition feature of the reproducing kernel approximation. Several numerical examples are provided to verify accuracy of the proposed formulation.