OpenAIRE is about to release its new face with lots of new content and services.
During September, you may notice downtime in services, while some functionalities (e.g. user registration, login, validation, claiming) will be temporarily disabled.
We apologize for the inconvenience, please stay tuned!
For further information please contact helpdesk[at]

fbtwitterlinkedinvimeoflicker grey 14rssslideshare1
Brownlee, R.; Houston, Paul; Levesley, J.; Rosswog, S. (2005)
Languages: English
Types: Article
Subjects: Mathematics - Numerical Analysis
In this paper we consider two sources of enhancement for the meshfree Lagrangian particle method smoothed particle hydrodynamics (SPH) by improving the accuracy of the particle approximation. Namely, we will consider shape functions constructed using: moving least-squares approximation (MLS); radial basis functions (RBF). Using MLS approximation is appealing because polynomial consistency of the particle approximation can be enforced. RBFs further appeal as they allow one to dispense with the smoothing-length -- the parameter in the SPH method which governs the number of particles within the support of the shape function. Currently, only ad hoc methods for choosing the smoothing-length exist. We ensure that any enhancement retains the conservative and meshfree nature of SPH. In doing so, we derive a new set of variationally-consistent hydrodynamic equations. Finally, we demonstrate the performance of the new equations on the Sod shock tube problem.
  • The results below are discovered through our pilot algorithms. Let us know how we are doing!

    • 1. R. K. Beatson and W. A. Light. Fast evaluation of radial basis functions: methods for two-dimensional polyharmonic splines. IMA J. Numer. Anal., 17(3):343{372, 1997.
    • 2. T. Belytschko, B. Krongauz, D. Organ, M. Fleming, and P. Krysl. Meshless methods: An overview and recent developments. Comput. Meth. Appl. Mech. Engrg., 139:3{47, 1996.
    • 3. J. Bonet and T.-S. L. Lok. Variational and momentum preservation aspects of smooth particle hydrodynamic formulations. Comput. Methods Appl. Mech. Engrg., 180(1-2):97{115, 1999.
    • 4. L. P. Bos and K. S·alkauskas. Moving least-squares are Backus-Gilbert optimal. J. Approx. Theory, 59(3):267{275, 1989.
    • 5. D. Brown, L. Ling, Kansa E., and J. Levesley. On approximate cardinal preconditioning methods for solving PDEs with radial basis functions. Eng. Anal. Bound. Elem., 29:343{353, 2005.
    • 6. R. A. Brownlee and W. A. Light. Approximation orders for interpolation by surface splines to rough functions. IMA J. Numer. Anal., 24(2):179{192, 2004.
    • 7. G. A. Dilts. Moving-least-squares-particle hydrodynamics. I. Consistency and stability. Internat. J. Numer. Methods Engrg., 44(8):1115{1155, 1999.
    • 8. G. A. Dilts. Moving least-squares particle hydrodynamics. II. Conservation and boundaries. Internat. J. Numer. Methods Engrg., 48(10):1503{1524, 2000.
    • 9. S. Marri and S. D. M. White. Smoothed particle hydrodynamics for galaxyformation simulations: improved treatments of multiphase gas, of star formation and of supernovae feedback. Mon. Not. R. Astron. Soc., 345:561{574, 2003.
    • 10. J. J. Monaghan. Smoothed particle hydrodynamics. Rep. Prog. Phys., 68:1703{ 1759, 2005.
    • 11. D. Price. Magnetic Fields in Astrophysics. Ph.d., Institute of Astronomy, University of Cambridge, August 2004.
    • 12. G. A. Sod. A survey of several ¯nite di®erence methods for systems of nonlinear hyperbolic conservation laws. J. Comput. Phys., 27(1):1{31, 1978.
    • 13. H. Wendland. Piecewise polynomial, positive de¯nite and compactly supported radial functions of minimal degree. Adv. Comput. Math., 4(4):389{396, 1995.
    • 14. H. Wendland. Local polynomial reproduction and moving least squares approximation. IMA J. Numer. Anal., 21(1):285{300, 2001.
  • No related research data.
  • No similar publications.

Share - Bookmark

Cite this article

Cookies make it easier for us to provide you with our services. With the usage of our services you permit us to use cookies.
More information Ok