FSISPH: An SPH formulation for impacts between dissimilar materials

Pearl, Jason M.; Raskin, Cody D.; Michael Owen, J.

doi:10.1016/j.jcp.2022.111533

Title: FSISPH: An SPH formulation for impacts between dissimilar materials

Abstract

Here, we present an SPH formulation with several new features designed to better model the fully-compressible interaction of dissimilar materials. We developed the new method to simulate the atmospheric entry and break-up of small celestial bodies in planetary atmospheres. The formulation uses a unity-based, density-energy discretization of the hydrodynamic conservation laws with linear-corrected kernel gradients. To account for variations in compressibility, we use an HLLC approximate Riemann solver to adjust the velocity gradient at material interfaces. To handle large transverse velocity discontinuities, we introduce a simple slip interface model that limits the artificial viscosity at material interfaces. Diffusion is optionally applied through the velocity gradient and this allows the density and specific thermal energy to evolve in a manner more consistent with the first law of thermodynamics in comparison to other more direct diffusion schemes. We also introduce a material-local second-order artificial conduction scheme used to smooth the specific thermal energy field. Material damage fits neatly under this framework by treating the damage front as a material interface. The method has been implemented as a solver, FSISPH, within the code, Spheral++, and is publicly available on github. We test our new solver on a number of classic shock, mixing, andmore »« less

Authors:

^[1]; Raskin, Cody D. ^[1]; Michael Owen, J. ^[1]

Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

Publication Date:: Fri Aug 12 00:00:00 EDT 2022

Research Org.:: Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)

Sponsoring Org.:: USDOE National Nuclear Security Administration (NNSA)

OSTI Identifier:: 1888099

Alternate Identifier(s):: OSTI ID: 1884602

Report Number(s):: LLNL-JRNL-831263
Journal ID: ISSN 0021-9991; 1047464; TRN: US2309872

Grant/Contract Number:: AC52-07NA27344

Resource Type:: Accepted Manuscript

Journal Name:: Journal of Computational Physics

Additional Journal Information:: Journal Volume: 469; Journal Issue: N/A; Journal ID: ISSN 0021-9991

Publisher:: Elsevier

Country of Publication:: United States

Language:: English

Subject:: 79 ASTRONOMY AND ASTROPHYSICS; 97 MATHEMATICS AND COMPUTING; smoothed particle hydrodynamics; hydrodynamic instabilities; multi-material; fluid-solid interaction

Citation Formats


                    Pearl, Jason M., Raskin, Cody D., and Michael Owen, J. FSISPH: An SPH formulation for impacts between dissimilar materials.  United States: N. p., 2022. 
Web.  doi:10.1016/j.jcp.2022.111533.

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                    Pearl, Jason M., Raskin, Cody D., & Michael Owen, J. FSISPH: An SPH formulation for impacts between dissimilar materials.  United States.  https://doi.org/10.1016/j.jcp.2022.111533

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                    Pearl, Jason M., Raskin, Cody D., and Michael Owen, J. Fri .  
"FSISPH: An SPH formulation for impacts between dissimilar materials".  United States.  https://doi.org/10.1016/j.jcp.2022.111533.  https://www.osti.gov/servlets/purl/1888099.

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@article{osti_1888099,

  title        = {FSISPH: An SPH formulation for impacts between dissimilar materials},

  author       = {Pearl, Jason M. and Raskin, Cody D. and Michael Owen, J.},

  abstractNote = {Here, we present an SPH formulation with several new features designed to better model the fully-compressible interaction of dissimilar materials. We developed the new method to simulate the atmospheric entry and break-up of small celestial bodies in planetary atmospheres. The formulation uses a unity-based, density-energy discretization of the hydrodynamic conservation laws with linear-corrected kernel gradients. To account for variations in compressibility, we use an HLLC approximate Riemann solver to adjust the velocity gradient at material interfaces. To handle large transverse velocity discontinuities, we introduce a simple slip interface model that limits the artificial viscosity at material interfaces. Diffusion is optionally applied through the velocity gradient and this allows the density and specific thermal energy to evolve in a manner more consistent with the first law of thermodynamics in comparison to other more direct diffusion schemes. We also introduce a material-local second-order artificial conduction scheme used to smooth the specific thermal energy field. Material damage fits neatly under this framework by treating the damage front as a material interface. The method has been implemented as a solver, FSISPH, within the code, Spheral++, and is publicly available on github. We test our new solver on a number of classic shock, mixing, and multi-material problem. The components we outline can significantly improve accuracy of SPH for problems with sharp contact discontinuities.},

  doi          = {10.1016/j.jcp.2022.111533},

  journal      = {Journal of Computational Physics},

  number       = N/A,

  volume       = 469,

  place        = {United States},

  year         = {Fri Aug 12 00:00:00 EDT 2022},

  month        = {Fri Aug 12 00:00:00 EDT 2022}

}

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In this paper, we present an anti-diffusive method dedicated to the simulation of interface flows on Cartesian grids involving an arbitrary number m of compressible components. Our work is two-fold: first, we introduce a m-component flow model that generalizes a classic two material five-equation model. In that way, interfaces are localized using color function discontinuities and a pressure equilibrium closure law is used to complete this new model. The resulting model is demonstrated to be hyperbolic under simple assumptions and consistent. Second, we present a discretization strategy for this model relying on a Lagrange–Remap scheme. Here, the projection step involvesmore »« less
https://doi.org/10.1016/J.JCP.2014.05.012
IMPROVED PERFORMANCES IN SUBSONIC FLOWS OF AN SPH SCHEME WITH GRADIENTS ESTIMATED USING AN INTEGRAL APPROACH

Journal Article Valdarnini, R., E-mail: valda@sissa.it - Astrophysical Journal

In this paper, we present results from a series of hydrodynamical tests aimed at validating the performance of a smoothed particle hydrodynamics (SPH) formulation in which gradients are derived from an integral approach. We specifically investigate the code behavior with subsonic flows, where it is well known that zeroth-order inconsistencies present in standard SPH make it particularly problematic to correctly model the fluid dynamics. In particular, we consider the Gresho–Chan vortex problem, the growth of Kelvin–Helmholtz instabilities, the statistics of driven subsonic turbulence and the cold Keplerian disk problem. We compare simulation results for the different tests with those obtained,more »« less
https://doi.org/10.3847/0004-637X/831/1/103
The Discrete Equation Method (DEM) for Fully Compressible, Two-Phase Flows in Ducts of Spatially Varying Cross-Section

Journal Article Berry, R A ; Saurel, R ; LeMetayer, O - Nuclear Engineering and Design

For the simulation of light water nuclear reactor coolant flows, general two-phase models (valid for all volume fractions) have been generally used which, while allowing for velocity disequilibrium, normally force pressure equilibrium between the phases (see, for example, the numerous models of this type described in H. Städtke, Gasdynamic Aspects of Two-Phase Flow, Wiley-VCH, 2006). These equations are not hyperbolic, their physical wave dynamics are incorrect, and their solution algorithms rely on dubious truncation error induced artificial viscosity to render them numerically well posed over a portion of the computational spectrum. The inherent problems of the traditional approach to multiphasemore »« less
https://doi.org/10.1016/j.nucengdes.2010.08.003
A robust and accurate approach to computing compressible multiphase flow: Stratified flow model and AUSM{sup +}-up scheme

Journal Article Chang, Chih-Hao ; Liou, Meng-Sing - Journal of Computational Physics

In this paper, we propose a new approach to compute compressible multifluid equations. Firstly, a single-pressure compressible multifluid model based on the stratified flow model is proposed. The stratified flow model, which defines different fluids in separated regions, is shown to be amenable to the finite volume method. We can apply the conservation law to each subregion and obtain a set of balance equations. Secondly, the AUSM{sup +} scheme, which is originally designed for the compressible gas flow, is extended to solve compressible liquid flows. By introducing additional dissipation terms into the numerical flux, the new scheme, called AUSM{sup +}-up,more »« less
https://doi.org/10.1016/j.jcp.2007.01.007
A simple and effective five-equation two-phase numerical model for liquid-vapor phase transition in cavitating flows

Journal Article Zhang, Ju - International Journal of Multiphase Flow

Numerical difficulties, notably the non-monotonic behavior of the Wood speed of sound and the volume fraction positivity, associated with the reduced five-equation two-phase flow model of Kapila et al. (2001) [A.K. Kapila, R. Menikoff, J.B. Bdzil, S.F. Son, D.S. Stewart, 2001. Two-phase modeling of deflagration-to-detonation transition in granular materials: reduced equations, Physics of Fluids 13(10), 3002–3024] have been resolved in the past through the introduction of a frozen speed of sound and an algebraic approach for mechanical relaxation afforded by a pressure non-equilibrium six-equation model proposed by [R. Saurel, F. Petitpas, R.A. Berry, 2009. Simple and efficient relaxation methods formore »« less
https://doi.org/10.1016/j.ijmultiphaseflow.2020.103417

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Title: FSISPH: An SPH formulation for impacts between dissimilar materials

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Citation Formats

Multiphase smoothed-particle hydrodynamics journal, May 2001

E pur si muove: Galilean-invariant cosmological hydrodynamical simulations on a moving mesh journal, January 2010

Modelling discontinuities and Kelvin–Helmholtz instabilities in SPH journal, December 2008

On the problem of penetration in particle methods journal, May 1989

Restoration of the contact surface in the HLL-Riemann solver journal, July 1994

An introduction to SPH journal, January 1988

Plane shock wave interaction with a cylindrical water column journal, May 2016

Phantom : A Smoothed Particle Hydrodynamics and Magnetohydrodynamics Code for Astrophysics journal, January 2018

Tensile strength and fracture energy of pressed metal powder by diametral compression test journal, July 2007

Improvements to the ɛ-α porous compaction model for simulating impacts into high-porosity solar system objects journal, June 2011

Continuum modelling of explosive fracture in oil shale journal, June 1980

Smoothed particle magnetohydrodynamics with a Riemann solver and the method of characteristics journal, November 2011

Explicit failure model for boron carbide ceramics under shock loading journal, August 2018

A Density-Independent Formulation of Smoothed Particle Hydrodynamics journal, April 2013

Smoothed particle hydrodynamics and magnetohydrodynamics journal, February 2012

Simulations of brittle solids using smooth particle hydrodynamics journal, May 1995

SPHGal: smoothed particle hydrodynamics with improved accuracy for galaxy simulations journal, July 2014

Moving least-squares particle hydrodynamics II: conservation and boundaries journal, January 2000

Formation of eccentric gas discs from sublimating or partially disrupted asteroids orbiting white dwarfs journal, May 2021

CWENO Finite-Volume Interface Capturing Schemes for Multicomponent Flows Using Unstructured Meshes journal, November 2021

An extension of Godunov SPH II: Application to elastic dynamics journal, March 2017

Particle methods in ocean and coastal engineering journal, September 2021

Smoothed Particle Hydrodynamics in Astrophysics journal, August 2010

Computations of Compressible Multifluids journal, May 2001

A numerical approach to the testing of the fission hypothesis journal, December 1977

Density-Independent Smoothed Particle Hydrodynamics for a Non-Ideal Equation of State journal, October 2013

Adaptive Smoothed Particle Hydrodynamics, with Application to Cosmology: Methodology journal, March 1996

Errors for calculations of strong shocks using an artificial viscosity and an artificial heat flux journal, September 1987

An SPH model for multiphase flows with complex interfaces and large density differences journal, February 2015

Moving-least-squares-particle hydrodynamics?I. Consistency and stability journal, March 1999

A Contact SPH Method with High-Order Limiters for Simulation of Inviscid Compressible Flows journal, August 2013

SPH without a Tensile Instability journal, April 2000

Implementations and tests of Godunov-type particle hydrodynamics journal, March 2003

A positivity-preserving high-order weighted compact nonlinear scheme for compressible gas-liquid flows journal, November 2021

The Lagrangian hydrodynamics code magma2 journal, August 2020

A survey of several finite difference methods for systems of nonlinear hyperbolic conservation laws journal, April 1978

A Well-Posed Kelvin-Helmholtz Instability test and Comparison journal, June 2012

A new class of accurate, mesh-free hydrodynamic simulation methods journal, April 2015

Chelyabinsk Airburst, Damage Assessment, Meteorite Recovery, and Characterization journal, November 2013

High velocity impact of metal sphere on thin metallic plates: A comparative smooth particle hydrodynamics study journal, February 2006

Smoothed Particle Hydrodynamics journal, September 1992

Numerical simulation of interfacial flows by smoothed particle hydrodynamics journal, November 2003

Simulation of Stationary Shock Waves in Porous Copper with Smoothed Particle Hydrodynamics journal, March 2021

A simple procedure to improve the pressure evaluation in hydrodynamic context using the SPH journal, June 2009

Kelvin-Helmholtz instabilities with Godunov smoothed particle hydrodynamics journal, April 2010

An extension of Godunov SPH: Application to negative pressure media journal, March 2016

On different calculation formulas of the pressure term in bi-phase SPH simulations journal, October 2018

Smoothed Particle Hydrodynamics: Some recent improvements and applications journal, December 1996

Smoothed particle hydrodynamics: theory and application to non-spherical stars journal, December 1977

Improving convergence in smoothed particle hydrodynamics simulations without pairing instability: SPH without pairing instability journal, August 2012

Flow visualization of shock/water column interactions journal, November 2007

Simulating surface tension with smoothed particle hydrodynamics journal, January 2000

Impact Simulations with Fracture. I. Method and Tests journal, January 1994

Smoothed particle hydrodynamics journal, July 2005

Multi-resolution Delta-plus-SPH with tensile instability control: Towards high Reynolds number flows journal, March 2018

Adaptive Smoothed Particle Hydrodynamics: Methodology. II. journal, June 1998

An incremental-stencil WENO reconstruction for simulation of compressible two-phase flows journal, July 2018

Hydrodynamic simulations with the Godunov smoothed particle hydrodynamics journal, September 2011

Smoothed particle hydrodynamics simulation of converging Richtmyer–Meshkov instability journal, August 2020

Improvements in SPH method by means of interparticle contact algorithm and analysis of perforation tests at moderate projectile velocities journal, September 2000

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

A compatibly differenced total energy conserving form of SPH: A COMPATIBLY DIFFERENCED TOTAL ENERGY CONSERVING FORM OF SPH journal, April 2014

CRKSPH – A Conservative Reproducing Kernel Smoothed Particle Hydrodynamics Scheme journal, March 2017

Numerical Simulations of Laboratory‐Scale, Hypervelocity‐Impact Experiments for Asteroid‐Deflection Code Validation journal, March 2020

Gasoline2: a modern smoothed particle hydrodynamics code journal, June 2017

Smoothed Particle Hydrodynamics Stability Analysis journal, January 1995

A general class of Lagrangian smoothed particle hydrodynamics methods and implications for fluid mixing problems journal, November 2012

A multi-phase SPH method for macroscopic and mesoscopic flows journal, April 2006

An overview of smoothed particle hydrodynamics for simulating multiphase flow journal, December 2016

A study of crack initiation and source mechanism in the Brazilian test based on moment tensor journal, April 2021

A constitutive model for metals applicable at high‐strain rate journal, March 1980

Numerical study of a planar shock interacting with a cylindrical water column embedded with an air cavity journal, July 2017

Fundamental differences between SPH and grid methods: Simulating fluids using SPH and grid techniques journal, August 2007

Instrumented Taylor anvil-on-rod impact tests for validating applicability of standard strength models to transient deformation states journal, October 2006

An incompressible multi-phase SPH method journal, November 2007

An improved SPH model for multiphase flows with large density ratios journal, July 2017

Shock simulation by the particle method SPH journal, November 1983

Multiphase smoothed-particle hydrodynamics
journal, May 2001

E pur si muove: Galilean-invariant cosmological hydrodynamical simulations on a moving mesh
journal, January 2010

Modelling discontinuities and Kelvin–Helmholtz instabilities in SPH
journal, December 2008

On the problem of penetration in particle methods
journal, May 1989

Restoration of the contact surface in the HLL-Riemann solver
journal, July 1994

An introduction to SPH
journal, January 1988

Plane shock wave interaction with a cylindrical water column
journal, May 2016

Phantom : A Smoothed Particle Hydrodynamics and Magnetohydrodynamics Code for Astrophysics
journal, January 2018

Tensile strength and fracture energy of pressed metal powder by diametral compression test
journal, July 2007

Improvements to the ɛ-α porous compaction model for simulating impacts into high-porosity solar system objects
journal, June 2011

Continuum modelling of explosive fracture in oil shale
journal, June 1980

Smoothed particle magnetohydrodynamics with a Riemann solver and the method of characteristics
journal, November 2011

Explicit failure model for boron carbide ceramics under shock loading
journal, August 2018

A Density-Independent Formulation of Smoothed Particle Hydrodynamics
journal, April 2013

Smoothed particle hydrodynamics and magnetohydrodynamics
journal, February 2012

Simulations of brittle solids using smooth particle hydrodynamics
journal, May 1995

SPHGal: smoothed particle hydrodynamics with improved accuracy for galaxy simulations
journal, July 2014

Moving least-squares particle hydrodynamics II: conservation and boundaries
journal, January 2000

Formation of eccentric gas discs from sublimating or partially disrupted asteroids orbiting white dwarfs
journal, May 2021

CWENO Finite-Volume Interface Capturing Schemes for Multicomponent Flows Using Unstructured Meshes
journal, November 2021

An extension of Godunov SPH II: Application to elastic dynamics
journal, March 2017

Particle methods in ocean and coastal engineering
journal, September 2021

Smoothed Particle Hydrodynamics in Astrophysics
journal, August 2010

Computations of Compressible Multifluids
journal, May 2001

A numerical approach to the testing of the fission hypothesis
journal, December 1977

Density-Independent Smoothed Particle Hydrodynamics for a Non-Ideal Equation of State
journal, October 2013

Adaptive Smoothed Particle Hydrodynamics, with Application to Cosmology: Methodology
journal, March 1996

Errors for calculations of strong shocks using an artificial viscosity and an artificial heat flux
journal, September 1987

An SPH model for multiphase flows with complex interfaces and large density differences
journal, February 2015

Moving-least-squares-particle hydrodynamics?I. Consistency and stability
journal, March 1999

A Contact SPH Method with High-Order Limiters for Simulation of Inviscid Compressible Flows
journal, August 2013

SPH without a Tensile Instability
journal, April 2000

Implementations and tests of Godunov-type particle hydrodynamics
journal, March 2003

A positivity-preserving high-order weighted compact nonlinear scheme for compressible gas-liquid flows
journal, November 2021

The Lagrangian hydrodynamics code magma2
journal, August 2020

A survey of several finite difference methods for systems of nonlinear hyperbolic conservation laws
journal, April 1978

A Well-Posed Kelvin-Helmholtz Instability test and Comparison
journal, June 2012

A new class of accurate, mesh-free hydrodynamic simulation methods
journal, April 2015

Chelyabinsk Airburst, Damage Assessment, Meteorite Recovery, and Characterization
journal, November 2013

High velocity impact of metal sphere on thin metallic plates: A comparative smooth particle hydrodynamics study
journal, February 2006

Smoothed Particle Hydrodynamics
journal, September 1992

Numerical simulation of interfacial flows by smoothed particle hydrodynamics
journal, November 2003

Simulation of Stationary Shock Waves in Porous Copper with Smoothed Particle Hydrodynamics
journal, March 2021

A simple procedure to improve the pressure evaluation in hydrodynamic context using the SPH
journal, June 2009

Kelvin-Helmholtz instabilities with Godunov smoothed particle hydrodynamics
journal, April 2010

An extension of Godunov SPH: Application to negative pressure media
journal, March 2016

On different calculation formulas of the pressure term in bi-phase SPH simulations
journal, October 2018

Smoothed Particle Hydrodynamics: Some recent improvements and applications
journal, December 1996

Smoothed particle hydrodynamics: theory and application to non-spherical stars
journal, December 1977

Improving convergence in smoothed particle hydrodynamics simulations without pairing instability: SPH without pairing instability
journal, August 2012

Flow visualization of shock/water column interactions
journal, November 2007

Simulating surface tension with smoothed particle hydrodynamics
journal, January 2000

Impact Simulations with Fracture. I. Method and Tests
journal, January 1994

Smoothed particle hydrodynamics
journal, July 2005

Multi-resolution Delta-plus-SPH with tensile instability control: Towards high Reynolds number flows
journal, March 2018

Adaptive Smoothed Particle Hydrodynamics: Methodology. II.
journal, June 1998

An incremental-stencil WENO reconstruction for simulation of compressible two-phase flows
journal, July 2018

Hydrodynamic simulations with the Godunov smoothed particle hydrodynamics
journal, September 2011

Smoothed particle hydrodynamics simulation of converging Richtmyer–Meshkov instability
journal, August 2020

Improvements in SPH method by means of interparticle contact algorithm and analysis of perforation tests at moderate projectile velocities
journal, September 2000

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

A compatibly differenced total energy conserving form of SPH: A COMPATIBLY DIFFERENCED TOTAL ENERGY CONSERVING FORM OF SPH
journal, April 2014

CRKSPH – A Conservative Reproducing Kernel Smoothed Particle Hydrodynamics Scheme
journal, March 2017

Numerical Simulations of Laboratory‐Scale, Hypervelocity‐Impact Experiments for Asteroid‐Deflection Code Validation
journal, March 2020

Gasoline2: a modern smoothed particle hydrodynamics code
journal, June 2017

Smoothed Particle Hydrodynamics Stability Analysis
journal, January 1995

A general class of Lagrangian smoothed particle hydrodynamics methods and implications for fluid mixing problems
journal, November 2012

A multi-phase SPH method for macroscopic and mesoscopic flows
journal, April 2006

An overview of smoothed particle hydrodynamics for simulating multiphase flow
journal, December 2016

A study of crack initiation and source mechanism in the Brazilian test based on moment tensor
journal, April 2021

A constitutive model for metals applicable at high‐strain rate
journal, March 1980

Numerical study of a planar shock interacting with a cylindrical water column embedded with an air cavity
journal, July 2017

Fundamental differences between SPH and grid methods: Simulating fluids using SPH and grid techniques
journal, August 2007

Instrumented Taylor anvil-on-rod impact tests for validating applicability of standard strength models to transient deformation states
journal, October 2006

An incompressible multi-phase SPH method
journal, November 2007

An improved SPH model for multiphase flows with large density ratios
journal, July 2017

Shock simulation by the particle method SPH
journal, November 1983

Homogeneous mixture model simulation of compressible multi-phase flows at all Mach number
journal, October 2021

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

Smoothed Particle Hydrodynamics Using Interparticle Contact Algorithms
journal, July 2002