An improved high-order ISPH method for simulation of free-surface flows and convection heat transfer

Abstract

The present work introduces a modified Incompressible Smoothed Particle Hydrodynamics (ISPH) model for simulation of free-surface flows and convection heat transfer. First, two new gradient and Laplacian models are proposed based on the Taylor series expansion and then used for discretization of the diffusion terms, Pressure Poisson's equation (PPE), and divergence of velocity. To maintain overall high-order accuracy, an explicit third-order TVD Runge-Kutta scheme is employed for discretization of the transient terms in Navier-Stokes and energy equations. Moreover, a new Hybrid Particle Shifting Technique (HPST) is developed by combining the classical PST and a collision model. A new kernel function is developed by combination of the Gaussian and polynomial functions and is then applied to the simulation of classical 1D Sod shock tube. Furthermore, a novel Hybrid Free-surface Detection (HFD) technique is proposed for accurate imposition of Dirichlet pressure boundary condition at the free surface area. The validity and applicability of proposed numerical schemes are verified against the several challenging benchmark cases including: dam-break flows with/without an obstacles, stretching water drop, rotating square patch of fluid, Rayleigh-Taylor instability, energy and exergy analysis of natural convection heat transfer in differentially heated cavity. The results show that, the newly constructed kernel function can successfully guarantee the stability and convergence of the numerical solution. Furthermore, it is found that, the proposed Hybrid Particle Shifting Technique (HPST) can efficiently resolve the unphysical discontinuity and suppress spurious pressure fluctuations.