Second order accurate particle-based formulations Explicit MPS-GS4-II family of algorithms for incompressible fluids with free surfaces

Masao Shimada, David Tae, Tao Xue, Rohit Deokar, K. K. Tamma

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

Purpose - The purpose of this paper is to present new implementation aspects of unified explicit time integration algorithms, called the explicit GS4-II family of algorithms, of a second-order time accuracy in all the unknowns (e.g. positions, velocities, and accelerations) with particular attention to the moving-particle simulation (MPS) method for solving the incompressible fluids with free surfaces. Design/methodology/approach - In the present paper, the explicit GS4-II family of algorithms is implemented in the MPS method in the following two different approaches: a direct explicit formulation with the use of the weak incompressibility equation involving the (modified) speed of sound; and a predictor-corrector explicit formulation. The first approach basically follows the concept of the explicit MPS method, presented in the literature, and the latter approach employs a similar concept used in, for example, a fractional-step method in computational fluid dynamics. Findings - Illustrative numerical examples demonstrate that any scheme within the proposed algorithmic framework captures the physics with the necessary second-order time accuracy and stability. Originality/value - The new algorithmic framework extended with the GS4-II family encompasses a multitude of pastand new schemes and offers a general purpose and unified implementation.

Original languageEnglish (US)
Pages (from-to)897-915
Number of pages19
JournalInternational Journal of Numerical Methods for Heat and Fluid Flow
Volume26
Issue number3-4
DOIs
StatePublished - May 3 2016

Bibliographical note

Funding Information:
Minnesota Supercomputing Institute (MSI) for computer grants. T. Xue acknowledges the support by the China Scholarship Council

Publisher Copyright:
© Emerald Group Publishing Limited.

Copyright:
Copyright 2016 Elsevier B.V., All rights reserved.

Keywords

  • Computational fluid dynamics
  • Incompressible fluids and free surfaces
  • Moving-particle simulation (mps) method
  • Time integration

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