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Title: CRKSPH – A Conservative Reproducing Kernel Smoothed Particle Hydrodynamics Scheme

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Publication Date:
Sponsoring Org.:
OSTI Identifier:
Grant/Contract Number:
AC02-06CH11357; AC52-07NA27344
Resource Type:
Journal Article: Published Article
Journal Name:
Journal of Computational Physics
Additional Journal Information:
Journal Volume: 332; Journal Issue: C; Related Information: CHORUS Timestamp: 2018-01-12 09:31:42; Journal ID: ISSN 0021-9991
Country of Publication:
United States

Citation Formats

Frontiere, Nicholas, Raskin, Cody D., and Owen, J. Michael. CRKSPH – A Conservative Reproducing Kernel Smoothed Particle Hydrodynamics Scheme. United States: N. p., 2017. Web. doi:10.1016/
Frontiere, Nicholas, Raskin, Cody D., & Owen, J. Michael. CRKSPH – A Conservative Reproducing Kernel Smoothed Particle Hydrodynamics Scheme. United States. doi:10.1016/
Frontiere, Nicholas, Raskin, Cody D., and Owen, J. Michael. Wed . "CRKSPH – A Conservative Reproducing Kernel Smoothed Particle Hydrodynamics Scheme". United States. doi:10.1016/
title = {CRKSPH – A Conservative Reproducing Kernel Smoothed Particle Hydrodynamics Scheme},
author = {Frontiere, Nicholas and Raskin, Cody D. and Owen, J. Michael},
abstractNote = {},
doi = {10.1016/},
journal = {Journal of Computational Physics},
number = C,
volume = 332,
place = {United States},
year = {Wed Mar 01 00:00:00 EST 2017},
month = {Wed Mar 01 00:00:00 EST 2017}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record at 10.1016/

Citation Metrics:
Cited by: 4works
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  • We present and test a new, special-relativistic formulation of smoothed particle hydrodynamics (SPH). Our approach benefits from several improvements with respect to earlier relativistic SPH formulations. It is self-consistently derived from the Lagrangian of an ideal fluid and accounts for the terms that stem from non-constant smoothing lengths, usually called 'grad-h terms'. In our approach, we evolve the canonical momentum and the canonical energy per baryon and thus circumvent some of the problems that have plagued earlier formulations of relativistic SPH. We further use a much improved artificial viscosity prescription which uses the extreme local eigenvalues of the Euler equationsmore » and triggers selectively on (a) shocks and (b) velocity noise. The shock trigger accurately monitors the relative density slope and uses it to fine-tune the amount of artificial viscosity that is applied. This procedure substantially sharpens shock fronts while still avoiding post-shock noise. If not triggered, the viscosity parameter of each particle decays to zero. None of these viscosity triggers is specific to special relativity, both could also be applied in Newtonian SPH. The performance of the new scheme is explored in a large variety of benchmark tests where it delivers excellent results. Generally, the grad-h terms deliver minor, though worthwhile, improvements. As expected for a Lagrangian method, it performs close to perfect in supersonic advection tests, but also in strong relativistic shocks, usually considered a particular challenge for SPH, the method yields convincing results. For example, due to its perfect conservation properties, it is able to handle Lorentz factors as large as {gamma} = 50,000 in the so-called wall shock test. Moreover, we find convincing results in a rarely shown, but challenging test that involves so-called relativistic simple waves and also in multi-dimensional shock tube tests.« less
  • Abstract not provided.
  • In the analysis of complex phenomena of acoustic systems, the computational modeling requires special attention in order to give a realistic representation of the physics. As a powerful tool, the finite element method has been widely used in the study of complex systems. In order to capture the important physical phenomena, p-finite elements and/or hp-finite elements are employed. The Reproducing Kernel Particle Methods (RKPM) are emerging as an effective alternative due to the absence of a mesh and the ability to analyze a specific frequency range. In this study, a wavelet particle method based on the multiresolution analysis encountered inmore » signal processing has been developed. The interpolation functions consist of spline functions with a built-in window which permits translation as well as dilation. A variation in the size of the window implies a geometrical refinement and allows the filtering of the desired frequency range. An adaptivity similar to hp-finite element method is obtained through the choice of an optimal dilation parameter. The analysis of the wave equation shows the effectiveness of this approach. The frequency/wave number relationship of the continuum case can be closely simulated by using the reproducing kernel particle methods. A similar methodology is also developed for the Timoshenko beam.« less
  • We show that the smoothed-particle-hydrodynamics discretization technique is compatible with the principles of general relativity if the contact interactions are modeled by spatial smoothing functions in the local frame comoving with the fluid. We then develop a smoothed-particle-hydrodynamics algorithm to model a non-self-gravitating isentropic fluid on a curved background. The equations of the fluid are discretized using a kernel whose spatial support is of a constant proper width in the local comoving frame. The one-dimensional relativistic shock problem is used for testing this algorithm.
  • Smoothed particle hydrodynamics (SPH) is formulated in two-dimensional axisymmetric coordinates. Starting with a three-dimensional Cartesian representation of SPH we integrate out the angular component and find a two-dimensional cylindrical description. A smoothed [open quotes]particle[close quotes] in this formulation becomes a smoothed [open quotes]torus.[close quotes] The hoop stress, resulting from interactions within the toroidal ring, is a natural consequence of the derivation. No pathological behavior is observed at the symmetry axis. The formulation has been extended to include the entire stress tensor, not just the pressure, and is therefore applicable to a wide range of materials and flow speeds. Three calculationsmore » are presented and compared to known results. 15 refs., 7 figs., 1 tab.« less