CRKSPH – A Conservative Reproducing Kernel Smoothed Particle Hydrodynamics Scheme
We present a formulation of smoothed particle hydrodynamics (SPH) that utilizes a firstorder consistent reproducing kernel, a smoothing function that exactly interpolates linear fields with particle tracers. Previous formulations using reproducing kernel (RK) interpolation have had difficulties maintaining conservation of momentum due to the fact the RK kernels are not, in general, spatially symmetric. Here in this paper, we utilize a reformulation of the fluid equations such that mass, linear momentum, and energy are all rigorously conserved without any assumption about kernel symmetries, while additionally maintaining approximate angular momentum conservation. Our approach starts from a rigorously consistent interpolation theory, where we derive the evolution equations to enforce the appropriate conservation properties, at the sacrifice of full consistency in the momentum equation. Additionally, by exploiting the increased accuracy of the RK method's gradient, we formulate a simple limiter for the artificial viscosity that reduces the excess diffusion normally incurred by the ordinary SPH artificial viscosity. Collectively, we call our suite of modifications to the traditional SPH scheme Conservative Reproducing Kernel SPH, or CRKSPH. CRKSPH retains many benefits of traditional SPH methods (such as preserving Galilean invariance and manifest conservation of mass, momentum, and energy) while improving on many of the shortcomingsmore »
 Authors:

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 Univ. of Chicago, IL (United States). Dept. of Physics; Argonne National Lab. (ANL), Argonne, IL (United States). High Energy Physics Division
 Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
 Publication Date:
 Report Number(s):
 LLNLJRNL690757
Journal ID: ISSN 00219991; 816805
 Grant/Contract Number:
 AC5207NA27344; AC0206CH11357
 Type:
 Published Article
 Journal Name:
 Journal of Computational Physics
 Additional Journal Information:
 Journal Volume: 332; Journal Issue: C; Journal ID: ISSN 00219991
 Publisher:
 Elsevier
 Research Org:
 Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
 Sponsoring Org:
 USDOE National Nuclear Security Administration (NNSA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 97 MATHEMATICS AND COMPUTING; 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Hydrodynamics; Meshfree
 OSTI Identifier:
 1337531
 Alternate Identifier(s):
 OSTI ID: 1468909
Frontiere, Nicholas, Raskin, Cody D., and Owen, J. Michael. CRKSPH – A Conservative Reproducing Kernel Smoothed Particle Hydrodynamics Scheme. United States: N. p.,
Web. doi:10.1016/j.jcp.2016.12.004.
Frontiere, Nicholas, Raskin, Cody D., & Owen, J. Michael. CRKSPH – A Conservative Reproducing Kernel Smoothed Particle Hydrodynamics Scheme. United States. doi:10.1016/j.jcp.2016.12.004.
Frontiere, Nicholas, Raskin, Cody D., and Owen, J. Michael. 2016.
"CRKSPH – A Conservative Reproducing Kernel Smoothed Particle Hydrodynamics Scheme". United States.
doi:10.1016/j.jcp.2016.12.004.
@article{osti_1337531,
title = {CRKSPH – A Conservative Reproducing Kernel Smoothed Particle Hydrodynamics Scheme},
author = {Frontiere, Nicholas and Raskin, Cody D. and Owen, J. Michael},
abstractNote = {We present a formulation of smoothed particle hydrodynamics (SPH) that utilizes a firstorder consistent reproducing kernel, a smoothing function that exactly interpolates linear fields with particle tracers. Previous formulations using reproducing kernel (RK) interpolation have had difficulties maintaining conservation of momentum due to the fact the RK kernels are not, in general, spatially symmetric. Here in this paper, we utilize a reformulation of the fluid equations such that mass, linear momentum, and energy are all rigorously conserved without any assumption about kernel symmetries, while additionally maintaining approximate angular momentum conservation. Our approach starts from a rigorously consistent interpolation theory, where we derive the evolution equations to enforce the appropriate conservation properties, at the sacrifice of full consistency in the momentum equation. Additionally, by exploiting the increased accuracy of the RK method's gradient, we formulate a simple limiter for the artificial viscosity that reduces the excess diffusion normally incurred by the ordinary SPH artificial viscosity. Collectively, we call our suite of modifications to the traditional SPH scheme Conservative Reproducing Kernel SPH, or CRKSPH. CRKSPH retains many benefits of traditional SPH methods (such as preserving Galilean invariance and manifest conservation of mass, momentum, and energy) while improving on many of the shortcomings of SPH, particularly the overly aggressive artificial viscosity and zerothorder inaccuracy. We compare CRKSPH to two different modern SPH formulations (pressure based SPH and compatibly differenced SPH), demonstrating the advantages of our new formulation when modeling fluid mixing, strong shock, and adiabatic phenomena.},
doi = {10.1016/j.jcp.2016.12.004},
journal = {Journal of Computational Physics},
number = C,
volume = 332,
place = {United States},
year = {2016},
month = {12}
}