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

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.

Citation

Shimada, M., Tae, D., Xue, T., Deokar, R. and Tamma, K.K. (2016), "Second order accurate particle-based formulations: Explicit MPS-GS4-II family of algorithms for incompressible fluids with free surfaces", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 26 No. 3/4, pp. 897-915. https://doi.org/10.1108/HFF-10-2015-0424