Dispersion Analysis of Smoothed Particle Hydrodynamics to Study Convergence and Numerical Phenomena at Coarse Resolution

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Abstract

The Smoothed Particle Hydrodynamics (SPH) method is a meshless Lagrangian method widely used in continuum mechanics simulation. Despite its wide application, theoretical issues of SPH approximation, stability, and convergence are among the unsolved problems of computational mathematics. In this paper, we present the application of dispersion analysis to the SPH approximation of one-dimensional gas dynamics equations to study numerical phenomena that appeared in practice. We confirmed that SPH converges only if the number of particles per wavelength increases while smoothing length decreases. At the same time, reduction of the smoothing length when keeping the number of particles in the kernel fixed (typical convergence results for finite differences and finite elements) does not guarantee the convergence of the numerical solution to the analytical one. We indicate the particular regimes with pronounced irreducible numerical dispersion. For coarse resolution, our theoretical findings are confirmed in simulations.

Original languageEnglish
Title of host publicationComputational Science and Its Applications - ICCSA 2022 - 22nd International Conference, Proceedings
EditorsOsvaldo Gervasi, Beniamino Murgante, Eligius M. Hendrix, David Taniar, Bernady O. Apduhan
PublisherSpringer Science and Business Media Deutschland GmbH
Pages184-197
Number of pages14
ISBN (Print)9783031105210
DOIs
Publication statusPublished - 2022
Event22nd International Conference on Computational Science and Its Applications, ICCSA 2022 - Malaga, Spain
Duration: 4 Jul 20227 Jul 2022

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume13375 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference22nd International Conference on Computational Science and Its Applications, ICCSA 2022
Country/TerritorySpain
CityMalaga
Period04.07.202207.07.2022

Keywords

  • Convergence analysis
  • Numerical dispersion
  • Smoothed particles hydrodynamics (SPH)

OECD FOS+WOS

  • 1.02 COMPUTER AND INFORMATION SCIENCES
  • 1.01 MATHEMATICS

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