Unique solvability and stability analysis for incompressible smoothed particle hydrodynamics method

Yusuke Imoto

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)

Abstract

The incompressible smoothed particle hydrodynamics (ISPH) method is a numerical method widely used for accurately and efficiently solving flow problems with free surface effects. However, to date there has been little mathematical investigation of properties such as stability or convergence for this method. In this paper, unique solvability and stability are mathematically analyzed for implicit and semi-implicit schemes in the ISPH method. Three key conditions for unique solvability and stability are introduced: a connectivity condition with respect to particle distribution and smoothing length, a regularity condition for particle distribution, and a time step condition. The unique solvability of both the implicit and semi-implicit schemes in two- and three-dimensional spaces is established with the connectivity condition. The stability of the implicit scheme in two-dimensional space is established with the connectivity and regularity conditions. Moreover, with the addition of the time step condition, the stability of the semi-implicit scheme in two-dimensional space is established. As an application of these results, modified schemes are developed by redefining discrete parameters to automatically satisfy parts of these conditions.

Original languageEnglish
Pages (from-to)297-309
Number of pages13
JournalComputational Particle Mechanics
Volume6
Issue number2
DOIs
Publication statusPublished - 2019 Apr 15
Externally publishedYes

Keywords

  • Incompressible Navier–Stokes equations
  • Incompressible smoothed particle hydrodynamics method
  • Stability
  • Unique solvability

ASJC Scopus subject areas

  • Computational Mechanics
  • Civil and Structural Engineering
  • Numerical Analysis
  • Modelling and Simulation
  • Fluid Flow and Transfer Processes
  • Computational Mathematics

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