Improved SPH methods for simulating free surface flows of viscous fluids

Abstract

In this paper we present two enhanced variants of the smoothed particle hydrodynamics (SPH) method for the numerical simulation of free surface flows of viscous fluids. Improvements are achieved by deriving a new set of general discrete SPH-like equations under an energy-based framework and applying a corrected (high-order) or coupled particle approximation scheme for function derivatives. By doing so, we ensure that the enhanced variants retain the conservative nature of SPH which is important for the stability of long-term simulations. Among various corrected approximations, we here implement the one obtained by the so-called finite particle method (FPM) within the framework to produce a higher-order SPH method which conserves both linear and angular momentums. In order to improve the efficiency of the higher-order variant, a coupled approach with the idea of using the SPH approximation for the interior particles and the FPM approximation for the exterior particles is also proposed and tested in this paper. Three prototype tests concerning free deformation of a viscous fluid patch with free surface are presented with comparisons between different methods to demonstrate the performance of the two proposed methods. Numerical results show that both the higher-order version using FPM and the coupled version using FPM/SPH outperform the original version of SPH in respect of accuracy and stability.

Numerical simulation of drop impact and jet buckling problems using the eXtended Pom–Pom model

“…Jiang et al [18] recently studied the impact of liquid droplets on solid surfaces using the multi-mode XPP model. In that work, the IMproved SPH method (IMSPH, see details of this method in [12]) was extended and tested in the simulation of viscoelastic free surface flows. However, in the context of the MAC approach, using finite differences and staggered grids, numerical predictions of drop impact of branched polymers have received relatively little attention, and to the authors' best knowledge, this is the first work to employ grid-based numerical methods for simulating drop impact using the XPP model.…”

SPH-Based Numerical Study of the Impact of Mudflows on Obstacles

“…This equation of state has been used previously on viscous flows with good results [Morris et al, 1997;Fang et al, 2009]. See also [Chambon et al, 2011] for a discussion of various equations of state used in previous studies.…”

Numerical modeling of flood waves in a bumpy channel with the different boundary conditions

“…However, in spite of successful use of both methods for treating free surface flows, numerical diffusion due to solving NSEs on a fixed Eulerian grid arose, especially when the deformation of free surface is very large [8]. In the general area of computational mechanics there is a growing interest in developing so-called meshless/ meshfree methods 3 or particle methods as alternatives to traditional grid-based methods such as finite difference methods and finite element methods [9]. One of the oldest mesh-less methods is the Smoothed Particle Hydrodynamics (SPH) method.…”