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

Huang, Tsung-Hui; Chen, Jiun-Shyan; Wei, Haoyan; Roth, Michael J.; Sherburn, Jesse A.; Bishop, Joseph E.; Tupek, Michael R.; Fang, Eliot H.

doi:10.1007/s40571-019-00248-x

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

Journal Article · 30 May 2019 · Computational Particle Mechanics

DOI: https://doi.org/10.1007/s40571-019-00248-x · OSTI ID:1526226

Huang, Tsung-Hui ^[1];

^[1]; Wei, Haoyan ^[1]; Roth, Michael J. ^[2]; Sherburn, Jesse A. ^[2]; Bishop, Joseph E. ^[3]; Tupek, Michael R. ^[3]; Fang, Eliot H. ^[3]

University of California, San Diego, La Jolla, CA (United States)
U.S. Army Engineer Research and Development Center, Vicksburg, MS (United States)
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

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.

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Research Organization:: Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA)

Grant/Contract Number:: AC04-94AL85000; NA0003525

OSTI ID:: 1526226

Report Number(s):: SAND--2019-5754J; 675750

Journal Information:: Computational Particle Mechanics, Journal Name: Computational Particle Mechanics Journal Issue: 2 Vol. 7; ISSN 2196-4378

Publisher:: Springer NatureCopyright Statement

Country of Publication:: United States

Language:: English

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