An incompressible smoothed particle hydrodynamics scheme for Newtonian/non‐Newtonian multiphase flows including semi‐analytical solutions for two‐phase inelastic Poiseuille flows

Abstract

An incompressible smoothed particle hydrodynamics (ISPH) method is developed for the modeling of multiphase Newtonian and inelastic non-Newtonian flows at low density ratios. This new method is the multiphase extension of Xenakis et al, J. Non-Newtonian Fluid Mech., 218, 1-15, which has been shown to be stable and accurate, with a virtually noise-free pressure field for single-phase non-Newtonian flows. For the validation of the method a semi-analytical solution of a two-phase Newtonian/non-Newtonian (inelastic) Poiseuille flow is derived. The developed method is also compared with the benchmark multiphase case of the Rayleigh Taylor instability and a submarine landslide, thereby demonstrating capability in both Newtonian/ Newtonian and Newtonian/non-Newtonian two-phase applications. Comparisons with analytical solutions, experimental and previously published results are conducted and show that the proposed methodology can accurately predict the free-surface and interface profiles of complex incompressible multi-phase flows at low-density ratios relevant, for example, to geophysical environmental applications. K E Y W O R D S incompressible SPH, inelastic non-Newtonian, landslides, multi-phase flows, semi-analytical two phase non-Newtonian 1 Int J Numer Meth Fluids. 2020;92:703-726. wileyonlinelibrary.com/journal/fld

An incompressible smoothed particle hydrodynamics‐finite volume method coupling algorithm for interface tracking of two‐phase fluid flows

“…In the time integration process of the ISPH-FVM method, the choice of the time step Δt is very important for the stability and the computational efficiency of the entire simulation process. The CFL (Courant-Friedrich-Lewy) condition 32,34,39 is adopted to estimate the time step size in this article. In the ISPH-FVM algorithm, the time step is constrained by the CFL conditions of both ISPH method and FVM method.…”

“…[25][26][27] In addition, the smoothed particle hydrodynamics (SPH) method has also been extended to investigate complex fluid problems such as two-phase flow. [28][29][30][31][32][33][34] Typical existing studies are as follows. Chen et al 28 developed an improved SPH multiphase model based on the assumption of pressure continuity on the interface.…”

“…The SPH method has the advantages in interface capturing and tracking, which has been widely used in free surface flows 25–27 . In addition, the smoothed particle hydrodynamics (SPH) method has also been extended to investigate complex fluid problems such as two‐phase flow 28–34 . Typical existing studies are as follows.…”

“…Rezavand et al 31 improved the ISPH scheme for a variety of multiphase problems with single and merging interfaces. A repulsive force on the multiphase interface between different fluid particles is adopted in work of Rezavand et al 31 Xenaki et al 32 developed an extended ISPH method for simulating multiphase Newtonian and inelastic non‐Newtonian flows at low density ratios. Rahmat et al 33 introduced the film drainage model and the leaky dielectric model into the ISPH method to simulate droplet coalescence and electric coalescence, which greatly expanded the application range of the ISPH method.…”

A GPU-Based δ-Plus-SPH Model for Non-Newtonian Multiphase Flows

“…However, current research has mainly focused on inviscid fluids and Newtonian fluid flow, whereas studies on SPH models for multiphase non-Newtonian flows are relatively scarce. Zainali et al [15] proposed a non-Newtonian multiphase incompressible smoothed particle hydrodynamics (ISPH) model by introducing an improved interface treatment procedure, and Xenakis et al [16] developed an ISPH model for non-Newtonian multiphase flows.…”