Improvement of the second order approximation of the smoothed particle hydrodynamics

2008 ◽  
Vol 13 (4) ◽  
pp. 404-407
Author(s):  
Si Chen ◽  
Dai Zhou ◽  
Shi-lin Dong ◽  
Hua-feng Li ◽  
Guang Yang
Keyword(s):  
Smoothed Particle Hydrodynamics ◽  
Order Approximation ◽  
Second Order ◽  
Second Order Approximation ◽  
Particle Hydrodynamics ◽  
Smoothed Particle

Numerical Simulation of Die Swell of Second-Order Fluids Using Smoothed Particle Hydrodynamics

2010 ◽  
Author(s):  
Samir Hassan Sadek ◽  
Mehmet Yildiz
Keyword(s):  
Free Surface ◽  
Smoothed Particle Hydrodynamics ◽  
Second Order ◽  
Rheological Parameters ◽  
Die Swell ◽  
Two Dimensional ◽  
Polymeric Fluid ◽  
Particle Hydrodynamics ◽  
Smoothed Particle ◽  
Second Order Fluids

This work presents the development of both weakly compressible and incompressible Smoothed Particle Hydrodynamics (SPH) models for simulating two-dimensional transient viscoelastic free surface flow which has extensive applications in polymer processing industries. As an illustration with industrial significance, we have chosen to model the extrudate swell of a second-order polymeric fluid. The extrudate or die swell is a phenomenon that takes place during the extrusion of polymeric fluids. When a polymeric fluid is forced through a die to give a polymer its desired shape, due to its viscoelastic non-Newtonian nature, it shows a tendency to swell or contract at the die exit depending on its rheological parameters. The die swell phenomenon is a typical example of a free surface problem where the free surface is formed at the die exit after the polymeric fluid has been extruded. The swelling process leads to an undesired increase in the dimensions of the extrudate. To be able to obtain a near-net shape product, the flow in the extrusion process should be well-understood to shed some light on the important process parameters behind the swelling phenomenon. To this end, a systematic study has been carried out to compare constitutive models proposed in literature for second-order fluids in terms of their ability to capture the physics behind the swelling phenomenon. The effect of various process and rheological parameters on the die swell such as the extrusion velocity, normal stress coefficients, and Reynolds and Deborah numbers have also been investigated. The models developed here can predict both swelling and contraction of the extrudate successfully. The die swell problem was solved for a wide range of Deborah numbers and for two different Re numbers. The numerical model was validated through the solution of fully developed Newtonian and Non-Newtonian viscoelastic flows in a two-dimensional channel, and the results of these two benchmark problems were compared with analytic solutions, and good agreements were obtained.

scholarly journals Modeling Free-surface Solitary Waves with Smoothed Particle Hydrodynamics

2017 ◽  
Author(s):  
Balázs Tóth
Keyword(s):  
Free Surface ◽  
Solitary Waves ◽  
Kdv Equation ◽  
Order Approximation ◽  
Three Dimensional ◽  
Order Theory ◽  
Second Order ◽  
Weakly Compressible ◽  
Particle Hydrodynamics ◽  
Smoothed Particle

A three-dimensional weakly compressible Smoothed ParticleHydrodynamics (SPH) solver is presented and applied tosimulate free-surface solitary waves generated in a quasi twodimensionaldam-break experiment. Test cases are constructedbased on the measurement layouts of a dam-break experiment.The simulated wave propagation speeds are compared to theexact solutions of the Korteweg-de Vries (KdV) equation as afirst order theory, and to a second order iterative approximationinvestigated in the literature. Free surface shapes of differentsimulation cases are investigated as well. The results show goodagreement with the free surface shapes of the KdV equation aswell as with the second order approximation of solitary wavepropagation speeds.

scholarly journals Second-Order Symmetric Smoothed Particle Hydrodynamics Method for Transient Heat Conduction Problems with Initial Discontinuity

Processes ◽  
2018 ◽  
Vol 6 (11) ◽  
pp. 215 ◽  
Author(s):  
Zhanjie Song ◽  
Yaxuan Xing ◽  
Qingzhi Hou ◽  
Wenhuan Lu
Keyword(s):  
Heat Conduction ◽  
Convergence Rate ◽  
Smoothed Particle Hydrodynamics ◽  
Transient Heat Conduction ◽  
Second Order ◽  
Order Convergence ◽  
Particle Hydrodynamics ◽  
Smoothed Particle ◽  
Initial Discontinuity ◽  
Second Order Convergence

To eliminate the numerical oscillations appearing in the first-order symmetric smoothed particle hydrodynamics (FO-SSPH) method for simulating transient heat conduction problems with discontinuous initial distribution, this paper presents a second-order symmetric smoothed particle hydrodynamics (SO-SSPH) method. Numerical properties of both SO-SSPH and FO-SSPH are analyzed, including truncation error, numerical accuracy, convergence rate, and stability. Experimental results show that for transient heat conduction with initial smooth distribution, both FO-SSPH and SO-SSPH can achieve second order convergence rate, which is consistent with the theoretical analysis. However, for one- and two-dimensional conduction with initial discontinuity, the FO-SSPH method suffers from serious unphysical oscillations, which do not disappear over time, and hence it only achieves a first-order convergence rate; while the present SO-SSPH method can avoid unphysical oscillations and has second-order convergence rate. Therefore, the SO-SSPH method is a feasible tool for solving transient heat conduction problems with both smooth and discontinuous distributions, and it is easy to be extended to high dimensional cases.

Modeling Die Swell of Second-Order Fluids Using Smoothed Particle Hydrodynamics

2013 ◽  
Vol 135 (5) ◽  
Author(s):  
Samir H. Sadek ◽  
Mehmet Yildiz
Keyword(s):  
Smoothed Particle Hydrodynamics ◽  
Polymer Processing ◽  
Second Order ◽  
Rheological Parameters ◽  
Die Swell ◽  
Two Dimensional ◽  
Wide Range ◽  
Particle Hydrodynamics ◽  
Smoothed Particle ◽  
Second Order Fluids

This work presents the development of a weakly compressible smoothed particle hydrodynamics (WCSPH) model for simulating two-dimensional transient viscoelastic free surface flow which has extensive applications in polymer processing industries. As an illustration for the capability of the model, the extrudate or die swell behaviors of second-order and Olyroyd-B polymeric fluids are studied. A systematic study has been carried out to compare constitutive models for second-order fluids available in literature in terms of their ability to capture the physics behind the swelling phenomenon. The effects of various process and rheological parameters on the die swell such as the extrusion velocity, normal stress coefficients, and Reynolds and Deborah numbers have also been investigated. The models developed here can predict both swelling and contraction of the extrudate successfully. The die swell of a second-order fluid was solved for a wide range of Deborah numbers and for two different Reynolds numbers. The numerical approach was validated through the solution of fully developed Newtonian and non-Newtonian viscoelastic flows in a two-dimensional channel as well as modeling the die swell of a Newtonian fluid. The results of these three benchmark problems were compared with analytic solutions and numerical results in literature when pertinent, and good agreements were obtained.

Simulations of slug impact with smoothed particle hydrodynamics: Some remarks on frequently asked questions

2000 ◽  
Vol 10 (PR9) ◽  
pp. Pr9-427-Pr9-432
Author(s):  
P. Galon ◽  
H. Bung ◽  
M. Lepareux ◽  
T. Grünenwald
Keyword(s):  
Smoothed Particle Hydrodynamics ◽  
Particle Hydrodynamics ◽  
Smoothed Particle

Simulation de l'écoulement au cours du procédé de rotomoulage par la méthode Smoothed Particle Hydrodynamics (SPH)

2008 ◽  
Vol 96 (6) ◽  
pp. 263-268 ◽  
Author(s):  
E. Mounif ◽  
V. Bellenger ◽  
A. Ammar ◽  
R. Ata ◽  
P. Mazabraud ◽  
...  
Keyword(s):  
Smoothed Particle Hydrodynamics ◽  
Particle Hydrodynamics ◽  
Smoothed Particle
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