An improved particle shifting technique for incompressible smoothed particle hydrodynamics methods

Abstract

Summary The smoothed particle hydrodynamics (SPH) method is one of the powerful Lagrangian tools for modeling free surface flows. However, it suffers from particle disorder, which leads to interpolation and numerical errors. To overcome this problem, several techniques have been introduced until now, among which the particle shifting technique (PST) based on Fick's law is an efficient one. The current form of this method needs tuning parameters to fulfill numerical stability criteria. In this study, to eliminate calibration factors, a new shifting coefficient is derived theoretically based on particle positions before and after shifting, regardless of other parameters such as velocity, pressure, time step intervals, etc. The only required input is particle positions, and the main concern is conserving particle densities in their updated positions. In addition to the proposed PST, a new distribution index (DI) is introduced for measuring the spatial uniformity of particles. Furthering the research, some novel treatments are also studied to improve particle movements near free surface boundary. The proposed idea is only assessed for ISPH method in this study, and its performance in other SPH schemes needs more investigations. Following this innovative method, it is validated by modeling different cases including dam break flow, paddle movement, and elliptical water drop. In all cases, particle arrangements have been improved by means of the modified shifting method. In that sense, good agreements between simulation results with experimental data, analytical solutions, and other numerical methods approve the ability of the developed method in simulating free surface flows.

Multi-phase fluid flow simulation by using peridynamic differential operator

“…The same problem also happens in the PD field, as explained by Silling et al (Silling et al, 2017). To avoid the particle clustering phenomenon or the instability problem, the particle shifting technology (PST) (Xu et al, 2009) is widely applied in the fluid flow simulations (Akbari, 2019;Lind et al, 2012;Mokos et al, 2017;Shadloo et al, 2012;Vacondio et al, 2013;Zhang et al, 2019). The particles will be nearly uniformly distributed after shifting;…”

“…4. For particle methods such as SPH, the instability problem may occur when the particle distribution becomes highly distorted (Akbari, 2019). The numerical errors induced by the irregular particle spacing may dominate the results especially in the later stage of the numerical simulations.…”

Wave Interaction and Overwash with a Flexible Plate by Smoothed Particle Hydrodynamics

“…In the ISPH scheme, Dirichlet boundary condition P = 0 at the free surface, pressure of SPH particles at the free surface is set to be zero [44]. There are a few algorithms used to identify free-surface SPH particles, such as the weighted density less than 0.9 of the fluid density [47],…”

“…Here, we adopt the latter in the simulations. In order to reduce particle clumping as well as stabilize the free surface due to lack of surface tension, an extra viscosity is applied for the free-surface particles [47]…”

Analysing the Effects of Non-newtonian Viscoelastic Fluid Flows on Stretching Surfaces with Suction

“…A workable improved particle shifting technique for incompressible smoothed particle hydrodynamics method was investigated by [22]. The particle shifting technique (PST) based on Fick's law was an efficient one.…”