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

Abstract

Here, 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. Finally, 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.

Authors:
 [1]; ORCiD logo [1];  [1];  [2];  [2];  [3];  [3];  [3]
  1. University of California, San Diego, La Jolla, CA (United States)
  2. U.S. Army Engineer Research and Development Center, Vicksburg, MS (United States)
  3. Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Publication Date:
Research Org.:
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA)
OSTI Identifier:
1526226
Report Number(s):
[SAND-2019-5754J]
[Journal ID: ISSN 2196-4378; 675750]
Grant/Contract Number:  
[AC04-94AL85000; NA0003525]
Resource Type:
Accepted Manuscript
Journal Name:
Computational Particle Mechanics
Additional Journal Information:
[Journal Name: Computational Particle Mechanics]; Journal ID: ISSN 2196-4378
Publisher:
Springer Nature
Country of Publication:
United States
Language:
English
Subject:
42 ENGINEERING; 97 MATHEMATICS AND COMPUTING; Shock modeling; Compressible flow; RKPM; Riemann-SCNI; MUSCL-SCNI; Oscillation limiter

Citation Formats

Huang, Tsung-Hui, Chen, Jiun-Shyan, Wei, Haoyan, Roth, Michael J., Sherburn, Jesse A., Bishop, Joseph E., Tupek, Michael R., and Fang, Eliot H. A MUSCL-SCNI approach for meshfree modeling of shock waves in fluids. United States: N. p., 2019. Web. doi:10.1007/s40571-019-00248-x.
Huang, Tsung-Hui, Chen, Jiun-Shyan, Wei, Haoyan, Roth, Michael J., Sherburn, Jesse A., Bishop, Joseph E., Tupek, Michael R., & Fang, Eliot H. A MUSCL-SCNI approach for meshfree modeling of shock waves in fluids. United States. doi:10.1007/s40571-019-00248-x.
Huang, Tsung-Hui, Chen, Jiun-Shyan, Wei, Haoyan, Roth, Michael J., Sherburn, Jesse A., Bishop, Joseph E., Tupek, Michael R., and Fang, Eliot H. Fri . "A MUSCL-SCNI approach for meshfree modeling of shock waves in fluids". United States. doi:10.1007/s40571-019-00248-x.
@article{osti_1526226,
title = {A MUSCL-SCNI approach for meshfree modeling of shock waves in fluids},
author = {Huang, Tsung-Hui and Chen, Jiun-Shyan and Wei, Haoyan and Roth, Michael J. and Sherburn, Jesse A. and Bishop, Joseph E. and Tupek, Michael R. and Fang, Eliot H.},
abstractNote = {Here, 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. Finally, 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.},
doi = {10.1007/s40571-019-00248-x},
journal = {Computational Particle Mechanics},
number = ,
volume = ,
place = {United States},
year = {2019},
month = {5}
}

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