An incompressible SPH method for simulation of unsteady viscoelastic free-surface flows

Rafiee, Ashkan; Manzari, Mehrdad T.; Hosseini, Mohammad

doi:10.1016/j.ijnonlinmec.2007.09.006

Cited by 96 publications

(61 citation statements)

References 29 publications

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“…The arbitrary-Lagrangian-Eulerian method has also been used to simulate the filament stretching [23,24] and extrudate swell [25,26] of viscoelastic liquids. Finally, a few works on the simulation of free-surface viscoelastic flows with the mesh-free smoothed particle hydrodynamics method have been reported in [27][28][29]. Each of these Lagrangian methods has its own advantages and drawbacks.…”

Section: Introductionmentioning

confidence: 99%

Numerical simulation of the planar extrudate swell of pseudoplastic and viscoelastic fluids with the streamfunction and the VOF methods

Comminal

Pimenta

Hattel

et al. 2018

Journal of Non-Newtonian Fluid Mechanics

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. Numerical simulation of the planar extrudate swell of pseudoplastic and viscoelastic fluids with the streamfunction and the VOF methods. Journal of Non-Newtonian Fluid Mechanics, 252, 1-18. DOI: 10.1016/j.jnnfm.2017 A B S T R A C TWe present an Eulerian free-surface flow solver for incompressible pseudoplastic and viscoelastic non-Newtonian fluids. The free-surface flow solver is based on the streamfunction flow formulation and the volume-of-fluid method. The streamfunction solver computes the vector potential of a solenoidal velocity field, which ensures by construction the mass conservation of the solution, and removes the pressure unknown. Pseudoplastic liquids are modelled with a Carreau model. The viscoelastic fluids are governed by differential constitutive models reformulated with the log-conformation approach, in order to preserve the positive-definiteness of the conformation tensor, and to circumvent the high Weissenberg number problem. The volume fraction of the fluid is advected with a geometric conservative unsplit scheme that preserves a sharp interface representation. For the sake of comparison, we also implemented an algebraic advection scheme for the liquid volume fraction. The proposed numerical method is tested by simulating the planar extrudate swell with the Carreau, Oldroyd-B and Giesekus constitutive models. The swell ratio of the extrudates are compared with the data available in the literature, as well as with numerical simulations performed with the open-source rheoTool toolbox in OpenFOAM ® . While the simulations of the generalized Newtonian fluids achieved mesh independence for all the methods tested, the flow simulations of the viscoelastic fluids are more sensitive to mesh refinement and the choice of numerical scheme. Moreover, the simulations of Oldroyd-B fluid flows above a critical Weissenberg number are prone to artificial surface instabilities. These numerical artifacts are due to discretization errors within the Eulerian surface-capturing method. However, the numerical issues arise from the stress singularity at the die exit corner, and the unphysical predictions of the Oldroyd-B model in the skin layer of the extrudate after the die exit, where large extensional deformations occur.

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Section: Introductionmentioning

confidence: 99%

Numerical simulation of the planar extrudate swell of pseudoplastic and viscoelastic fluids with the streamfunction and the VOF methods

Comminal

Pimenta

Hattel

et al. 2018

Journal of Non-Newtonian Fluid Mechanics

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“…Shao et al (2006), Rafiee et al (2007), AtaieAshtiani and Shobeyri (2008), and Khayyer et al (2008). It is noted here that the density in Eqs.…”

Section: Lp-sph01mentioning

confidence: 67%

A review on approaches to solving Poisson’s equation in projection-based meshless methods for modelling strongly nonlinear water waves

Zhou

Yan

2016

J. Ocean Eng. Mar. Energy

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Three meshless methods, including incompressible smooth particle hydrodynamic (ISPH), moving particle semi-implicit (MPS) and meshless local Petrov-Galerkin method based on Rankine source solution (MLPG_R) methods, are often employed to model nonlinear or violent water waves and their interaction with marine structures. They are all based on the projection procedure, in which solving Poisson's equation about pressure at each time step is a major task. There are three different approaches to solving Poisson's equation, i.e. (1) discretizing Laplacian directly by approximating the second-order derivatives, (2) transferring Poisson's equation into a weak form containing only gradient of pressure and (3) transferring Poisson's equation into a weak form that does not contain any derivatives of functions to be solved. The first approach is often adopted in ISPH and MPS, while the third one is implemented by the MLPG_R method. This paper attempts to review the most popular, though not all, approaches available in literature for solving the equation.

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“…Alternatively, the Navier-Stokes equations are augmented with a term accounting for elastic forces, e.g. [Goktekin et al 2004] for grids, [Wojtan and Turk 2008] for FEM or [Rafiee et al 2007;Chang et al 2009;Chang et al 2011] for SPH. [Clavet et al 2005] simulated viscoelastic material with springbased viscosity forces that, however, do not consider shear rates.…”

Section: Viscosity In Multiphase Fluidsmentioning

confidence: 99%

An implicit viscosity formulation for SPH fluids

et al. 2015

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Figure 1: Interaction of a highly viscous fluid with complex moving solids. Up to 780k particles are used. The computation time is 30s per frame. AbstractWe present a novel implicit formulation for highly viscous fluids simulated with Smoothed Particle Hydrodynamics SPH. Compared to explicit methods, our formulation is significantly more efficient and handles a larger range of viscosities. Differing from existing implicit formulations, our approach reconstructs the velocity field from a target velocity gradient. This gradient encodes a desired shear-rate damping and preserves the velocity divergence that is introduced by the SPH pressure solver to counteract density deviations. The target gradient ensures that pressure and viscosity computation do not interfere. Therefore, only one pressure projection step is required, which is in contrast to state-of-the-art implicit Eulerian formulations. While our model differs from true viscosity in that vorticity diffusion is not encoded in the target gradient, it nevertheless captures many of the qualitative behaviors of viscous liquids. Our formulation can easily be incorporated into complex scenarios with one-and two-way coupled solids and multiple fluid phases with different densities and viscosities.

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An incompressible SPH method for simulation of unsteady viscoelastic free-surface flows

Cited by 96 publications

References 29 publications

Numerical simulation of the planar extrudate swell of pseudoplastic and viscoelastic fluids with the streamfunction and the VOF methods

Numerical simulation of the planar extrudate swell of pseudoplastic and viscoelastic fluids with the streamfunction and the VOF methods

A review on approaches to solving Poisson’s equation in projection-based meshless methods for modelling strongly nonlinear water waves

An implicit viscosity formulation for SPH fluids

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