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

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:

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)

Publication Date:: 2019-05-31

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 Volume: 7; Journal Issue: 2; 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.

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                    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.  https://doi.org/10.1007/s40571-019-00248-x

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                    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.  https://doi.org/10.1007/s40571-019-00248-x.  https://www.osti.gov/servlets/purl/1526226.

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@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       = 2,

  volume       = 7,

  place        = {United States},

  year         = {2019},

  month        = {5}

}

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Works referencing / citing this record:

RKPM2D: an open-source implementation of nodally integrated reproducing kernel particle method for solving partial differential equations
journal, August 2019

Huang, Tsung-Hui; Wei, Haoyan; Chen, Jiun-Shyan
Computational Particle Mechanics, Vol. 7, Issue 2
DOI: 10.1007/s40571-019-00272-x

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

Abstract

Citation Formats

Hydrodynamic meshfree method for high-rate solid dynamics using a Rankine-Hugoniot enhancement in a Riemann-SCNI framework: HYDRODYNAMIC MESHFREE METHOD journal, May 2016

Uniformly high order accurate essentially non-oscillatory schemes, III journal, August 1987

On Upstream Differencing and Godunov-Type Schemes for Hyperbolic Conservation Laws journal, January 1983

Linear Elastic Response of Tubes to Internal Detonation Loading journal, May 2002

Flux vector splitting of the inviscid gasdynamic equations with application to finite-difference methods journal, April 1981

Numerical Instabilities in Upwind Methods: Analysis and Cures for the “Carbuncle” Phenomenon journal, January 2001

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A Damage Particle Method for Smeared Modeling of Brittle Fracture journal, January 2018

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A finite point method for adaptive three-dimensional compressible flow calculations journal, July 2009

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On the shock-vortex interaction in Schardin's problem journal, November 2000

Use of artificial viscosity in multidimensional fluid dynamic calculations journal, July 1980

A stabilized conforming nodal integration for Galerkin mesh-free methods journal, January 2000

A general, non-iterative Riemann solver for Godunov's method journal, October 1985

Towards the ultimate conservative difference scheme. V. A second-order sequel to Godunov's method journal, July 1979

Robust HLL-type Riemann solver capable of resolving contact discontinuity journal, June 2012

VI. On the rate of explosion in gases journal, January 1899

Numerical solutions of Euler equations by using a new flux vector splitting scheme journal, July 1993

Reproducing Kernel Particle Methods for large deformation analysis of non-linear structures journal, December 1996

Towards the ultimate conservative difference scheme. II. Monotonicity and conservation combined in a second-order scheme journal, March 1974

The weighted reconstruction of reproducing kernel particle method for one-dimensional shock wave problems journal, February 2018

The design and application of upwind schemes on unstructured meshes conference, February 2013

Flux splitting schemes for the Euler equations journal, November 2012

Total variation diminishing Runge-Kutta schemes journal, January 1998

High Frequency Cinematography in the Shock Tube journal, January 1957

A finite point method for compressible flow: A FINITE POINT METHOD FOR COMPRESSIBLE FLOW journal, December 2001

A New Flux Splitting Scheme journal, July 1993

A new class of Moving-Least-Squares WENO–SPH schemes journal, August 2014

Simplified Second-Order Godunov-Type Methods journal, May 1988

Uniformly High-Order Accurate Nonoscillatory Schemes. I journal, April 1987

Shock simulation by the particle method SPH journal, November 1983

Towards the ultimate conservative difference scheme. IV. A new approach to numerical convection journal, March 1977

Efficient Implementation of Weighted ENO Schemes journal, June 1996

A Finite-Volume Particle Method for Compressible Flows journal, December 2000

A Method for the Numerical Calculation of Hydrodynamic Shocks journal, March 1950

SPH and Riemann Solvers journal, September 1997

A stabilized nodally integrated meshfree formulation for fully coupled hydro-mechanical analysis of fluid-saturated porous media journal, December 2016

Reformulation of Smoothed Particle Hydrodynamics with Riemann Solver journal, June 2002

Filters, reproducing kernel, and adaptive meshfree method journal, July 2003

Reproducing kernel particle methods journal, April 1995

Uniformly High Order Accurate Essentially Non-oscillatory Schemes, III journal, February 1997

Approximate Riemann Solvers, Parameter Vectors, and Difference Schemes journal, August 1997

A contribution to the great Riemann solver debate journal, March 1994

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Hydrodynamic meshfree method for high-rate solid dynamics using a Rankine-Hugoniot enhancement in a Riemann-SCNI framework: HYDRODYNAMIC MESHFREE METHOD
journal, May 2016

Uniformly high order accurate essentially non-oscillatory schemes, III
journal, August 1987

On Upstream Differencing and Godunov-Type Schemes for Hyperbolic Conservation Laws
journal, January 1983

Linear Elastic Response of Tubes to Internal Detonation Loading
journal, May 2002

Flux vector splitting of the inviscid gasdynamic equations with application to finite-difference methods
journal, April 1981

Numerical Instabilities in Upwind Methods: Analysis and Cures for the “Carbuncle” Phenomenon
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Stable and flux-conserved meshfree formulation to model shocks
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A Damage Particle Method for Smeared Modeling of Brittle Fracture
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Approximate Riemann solvers, parameter vectors, and difference schemes
journal, October 1981

Efficient implementation of essentially non-oscillatory shock-capturing schemes
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A finite point method for adaptive three-dimensional compressible flow calculations
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Meshfree Methods: Progress Made after 20 Years
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On the shock-vortex interaction in Schardin's problem
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Use of artificial viscosity in multidimensional fluid dynamic calculations
journal, July 1980

A stabilized conforming nodal integration for Galerkin mesh-free methods
journal, January 2000

A general, non-iterative Riemann solver for Godunov's method
journal, October 1985

Towards the ultimate conservative difference scheme. V. A second-order sequel to Godunov's method
journal, July 1979

Robust HLL-type Riemann solver capable of resolving contact discontinuity
journal, June 2012

VI. On the rate of explosion in gases
journal, January 1899

Numerical solutions of Euler equations by using a new flux vector splitting scheme
journal, July 1993

Reproducing Kernel Particle Methods for large deformation analysis of non-linear structures
journal, December 1996

Towards the ultimate conservative difference scheme. II. Monotonicity and conservation combined in a second-order scheme
journal, March 1974

The weighted reconstruction of reproducing kernel particle method for one-dimensional shock wave problems
journal, February 2018

The design and application of upwind schemes on unstructured meshes
conference, February 2013

Flux splitting schemes for the Euler equations
journal, November 2012

Total variation diminishing Runge-Kutta schemes
journal, January 1998

High Frequency Cinematography in the Shock Tube
journal, January 1957

A finite point method for compressible flow: A FINITE POINT METHOD FOR COMPRESSIBLE FLOW
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A New Flux Splitting Scheme
journal, July 1993

A new class of Moving-Least-Squares WENO–SPH schemes
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Simplified Second-Order Godunov-Type Methods
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Uniformly High-Order Accurate Nonoscillatory Schemes. I
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Shock simulation by the particle method SPH
journal, November 1983

Towards the ultimate conservative difference scheme. IV. A new approach to numerical convection
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Efficient Implementation of Weighted ENO Schemes
journal, June 1996

A Finite-Volume Particle Method for Compressible Flows
journal, December 2000

A Method for the Numerical Calculation of Hydrodynamic Shocks
journal, March 1950

SPH and Riemann Solvers
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A stabilized nodally integrated meshfree formulation for fully coupled hydro-mechanical analysis of fluid-saturated porous media
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Reformulation of Smoothed Particle Hydrodynamics with Riemann Solver
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A contribution to the great Riemann solver debate
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journal, August 2019