Skip to main content
Disciplines
Automotive Business IT + Informatics Construction + Real Estate Electrical Engineering + Electronics Energy + Sustainability Insurance + Risk Finance + Banking Management + Leadership Marketing + Sales Mechanical Engineering + Materials
Events
DE
EN
Books
Journals
Topic Page
Marketing
Start single access now
Access for companies
EXTENDED SEARCH
Log in
Top
Computational Mechanics
Published in: Computational Mechanics 5/2018

12-01-2018 | Original Paper

A technique to remove the tensile instability in weakly compressible SPH

Authors: Xiaoyang Xu, Peng Yu

Published in: Computational Mechanics | Issue 5/2018

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

When smoothed particle hydrodynamics (SPH) is directly applied for the numerical simulations of transient viscoelastic free surface flows, a numerical problem called tensile instability arises. In this paper, we develop an optimized particle shifting technique to remove the tensile instability in SPH. The basic equations governing free surface flow of an Oldroyd-B fluid are considered, and approximated by an improved SPH scheme. This includes the implementations of the correction of kernel gradient and the introduction of Rusanov flux into the continuity equation. To verify the effectiveness of the optimized particle shifting technique in removing the tensile instability, the impacting drop, the injection molding of a C-shaped cavity, and the extrudate swell, are conducted. The numerical results obtained are compared with those simulated by other numerical methods. A comparison among different numerical techniques (e.g., the artificial stress) to remove the tensile instability is further performed. All numerical results agree well with the available data.
previous article An efficient hydro-mechanical model for coupled multi-porosity and discrete fracture porous media
next article Efficient numerical method with a dual-grid scheme for contact of inhomogeneous materials and its applications

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

inform now
Literature
1.
Hirt CW, Nicholls BD (1981) Volume of fluid (VOF) method for dynamics of free boundaries. J Comput Phys 39:201–221CrossRef
2.
McKee S, Tomé MF, Ferreira VG, Cuminato JA, Castelo A, Sousa FS, Mangiavacchi N (2008) The MAC method. Comput Fluids 37:907–930MathSciNetCrossRef
3.
Osher S, Sethian JA (1988) Fronts propagating with curvature-dependent speed: algorithms based on Hamilton Jacobi formulations. J Comput Phys 79:12–49MathSciNetCrossRef
4.
Li S, Liu WK (2002) Meshfree and particle methods and their applications. Appl Mech Rev 55:1–34CrossRef
5.
Li S, Liu WK (2004) Meshfree particle methods. Springer, BerlinMATH
6.
Liu MB, Liu GR (2010) Smoothed particle hydrodynamics (SPH): an overview and recent developments. Arch Comput Methods Eng 17:25–76MathSciNetCrossRef
7.
Gingold RA, Monaghan JJ (1977) Smoothed particle hydrodynamics theory and application to non-spherical stars. Mon Not R Astron Soc 181:375–389CrossRef
8.
Lucy LB (1977) A numerical approach to the testing of the fission hypothesis. Astron J 83:1013–1024CrossRef
9.
Shadloo MS, Zainali A, Sadek SH, Yildiz M (2011) Improved incompressible smoothed particle hydrodynamics method for simulating flow around bluff bodies. Comput Methods Appl Mech Eng 200:1008–1020MathSciNetCrossRef
10.
Shadloo MS, Zainali A, Yildiz M, Suleman A (2012) A robust weakly compressible SPH method and its comparison with an incompressible SPH. Int J Numer Methods Eng 89:939–956MathSciNetCrossRef
11.
Monaghan JJ (1994) Simulating free surface flows with SPH. J Comput Phys 110:399–406CrossRef
12.
Ozbulut M, Yildiz M, Goren O (2014) A numerical investigation into the correction algorithms for SPH method in modeling violent free surface flows. Int J Mech Sci 79:56–65CrossRef
13.
Xu X, Ouyang J, Jiang T, Li Q (2014) Numerical analysis of the impact of two droplets with a liquid film using an incompressible SPH method. J Eng Math 85:35–53MathSciNetCrossRef
14.
Xu X, Deng XL (2016) An improved weakly compressible SPH method for simulating free surface flows of viscous and viscoelastic fluids. Comput Phys Commun 201:43–62MathSciNetCrossRef
15.
Monaghan JJ, Kocharyan A (1995) SPH simulation of multi-phase flow. Comput Phys Commun 87:225–235CrossRef
16.
Zainali A, Tofighi N, Shadloo MS, Yildiz M (2013) Numerical investigation of Newtonian and non-Newtonian multiphase flows using ISPH method. Comput Methods Appl Mech Eng 254:99–113MathSciNetCrossRef
17.
Lind SJ, Stansby PK, Rogers BD (2016) Incompressible-compressible flows with a transient discontinuous interface using smoothed particle hydrodynamics (SPH). J Comput Phys 309:129–147MathSciNetCrossRef
18.
Tartakovskya AM, Panchenko A (2016) Pairwise force smoothed particle hydrodynamics model for multiphase flow: surface tension and contact line dynamics. J Comput Phys 305:1119–1146MathSciNetCrossRef
19.
Ellero M, Kroger M, Hess S (2002) Viscoelastic flows studied by smoothed particle dynamics. J Non-Newton Fluid Mech 105:35–51CrossRef
20.
Ellero M, Tanner RI (2005) SPH simulations of transient viscoelastic flows at low Reynolds number. J Non-Newton Fluid Mech 132:61–72CrossRef
21.
Xu X, Ouyang J, Jiang T, Li Q (2012) Numerical simulation of 3D-unsteady viscoelastic free surface flows by improved smoothed particle hydrodynamics method. J Non-Newton Fluid Mech 177:109–120CrossRef
22.
Xu X, Ouyang J (2013) A SPH-based particle method for simulating 3D transient free surface flows of branched polymer melts. J Non-Newton Fluid Mech 202:54–71CrossRef
23.
Xu X, Ouyang J, Liu Q, Li W (2014) SPH simulations of 2D transient viscoelastic flows using Brownian configuration fields. J Non-Newton Fluid Mech 208:59–71CrossRef
24.
Xu X, Yu P (2016) A multiscale SPH method for simulating transient viscoelastic flows using bead-spring chain model. J Non-Newton Fluid Mech 229:27–42MathSciNetCrossRef
25.
26.
Li S, Liu WK (1999) Reproducing kernel hierarchical partition of unity, part I—formulation and theory. Int J Numer Methods Eng 45:251–288CrossRef
27.
Li S, Liu WK (1999) Reproducing kernel hierarchical partition of unity, part II—applications. Int J Numer Methods Eng 45:289–317CrossRef
28.
Chen JK, Beraun JE, Jih CJ (1999) An improvement for tensile instability in smoothed particle hydrodynamics. Comput Mech 23:279–287CrossRef
29.
Chen JK, Beraun JE (2000) A generalized smoothed particle hydrodynamics method for nonlinear dynamic problems. Comput Methods Appl Mech Eng 190:225–239CrossRef
30.
Bonet J, Lok T-SL (1999) Variational and momentum preservation aspects of smooth particle hydrodynamic formulations. Comput Methods Appl Mech Eng 180:97–115MathSciNetCrossRef
31.
Liu MB, Xie WP, Liu GR (2005) Modeling incompressible flows using a finite particle method. Appl Math Model 29:1252–1270CrossRef
32.
Liu MB, Liu GR (2006) Restoring particle consistency in smoothed particle hydrodynamics. Appl Numer Math 56:19–36MathSciNetCrossRef
33.
Zhang GM, Batra RC (2004) Modified smoothed particle hydrodynamics method and its applications to transient problems. Comput Mech 34:137–146MATH
34.
Zhang GM, Batra RC (2007) Wave propagation in functionally graded materials by modified smoothed particle hydrodynamics (MSPH) method. J Comput Phys 222:374–390MathSciNetCrossRef
35.
Batra RC, Zhang GM (2007) Search algorithm and simulation of elastodynamic crack propagation by modified smoothed particle hydrodynamics (MSPH) method. Comput Mech 40:531–546CrossRef
36.
Fang J, Parriaux A, Rentschler M, Ancey C (2009) Improved SPH methods for simulating free surface flows of viscous fluids. Appl Numer Math 59(2):251–271MathSciNetCrossRef
37.
Xu R, Stansby PK, Laurence D (2009) Accuracy and stability in incompressible SPH (ISPH) based on the projection method and a new approach. J Comput Phys 228(18):6703–6725MathSciNetCrossRef
38.
Lind SJ, Xu R, Stansby PK, Rogers BD (2012) Incompressible smoothed particle hydrodynamics for free-surface flows: a generalised diffusion-based algorithm for stability and validations for impulsive flows and propagating waves. J Comput Phys 231(4):1499–1523MathSciNetCrossRef
39.
Skillen A, Lind S, Stansby PK, Rogers BD (2013) Incompressible smoothed particle hydrodynamics (SPH) with reduced temporal noise and generalised Fickian smoothing applied to body-water slam and efficient wave-body interaction. Comput Methods Appl Mech Eng 265:163–173MathSciNetCrossRef
40.
Xenakis AM, Lind SJ, Stansby PK, Rogers BD (2015) An incompressible SPH scheme with improved pressure predictions for free-surface generalised Newtonian flows. J Non-Newton Fluid Mech 218:1–15MathSciNetCrossRef
41.
Vila JP (1999) On particle weighted methods and smooth particle hydrodynamics. Math Model Methods Appl Sci 9:161–209MathSciNetCrossRef
42.
Ferrari A, Dumbser M, Toro EF, Armanini A (2009) A new 3D parallel SPH scheme for free-surface flows. Comput Fluids 38:1203–1217MathSciNetCrossRef
43.
Cherfils JM, Pinon G, Rivoalen E (2012) JOSEPHINE: a parallel SPH code for free surface flows. Comput Phys Commun 183:1468–1480MathSciNetCrossRef
44.
Cha SH, Inutsuka S, Nayakshin S (2010) Kelvin–Helmholtz instabilities with Godunov smoothed particle hydrodynamics. Mon Not R Astron Soc 403:1165–1174CrossRef
45.
Sugiura K, Inutsuka S (2016) An extension of Godunov SPH: application to negative pressure media. J Comput Phys 308:171–197MathSciNetCrossRef
46.
Sugiura K, Inutsuka S (2017) An extension of Godunov SPH II: application to elastic dynamics. J Comput Phys 333:78–103MathSciNetCrossRef
47.
Molteni D, Colagrossi A (2009) A simple procedure to improve the pressure evaluation in hydrodynamic context using the SPH. Comput Phys Commun 180:861–872MathSciNetCrossRef
48.
Antuono M, Colagrossi A, Marrone S, Molteni D (2010) Free-surface flows solved by means of SPH schemes with numerical diffusive terms. Comput Phys Commun 181:532–549MathSciNetCrossRef
49.
Marrone S, Antuono M, Colagrossi A, Colicchio G, Le Touzé D, Graziani G (2011) \(\delta \)-SPH model for simulating violent impact flows. Comput Methods Appl Mech Eng 200:1526–1542MathSciNetCrossRef
50.
Antuono M, Marrone S, Colagrossi A, Bouscasse B (2015) Energy balance in the \(\delta \)-SPH scheme. Comput Methods Appl Mech Eng 289:209–226MathSciNetCrossRef
51.
Sun PN, Colagrossi A, Marrone S et al (2017) The \(\delta \)plus-SPH model: simple procedures for a further improvement of the SPH scheme. Comput Methods Appl Mech Eng 315:25–49MathSciNetCrossRef
52.
Schuessler I, Schmitt D (1981) Comments on smoothed particle hydrodynamics. Astron Astrophys 97:373–379
53.
Swegle JW, Hicks DL, Attaway SW (1995) Smoothed particle hydrodynamics stability analysis. J Comput Phys 116:123–134MathSciNetCrossRef
54.
Dyka CT, Ingel RP (1995) An approach for tension instability in smoothed particle hydrodynamics (SPH). Comput Struct 57:573–580CrossRef
55.
Dyka CT, Randles PW, Ingel RP (1997) Stress points for tension instability in SPH. Int J Numer Methods Eng 40:2325–2341CrossRef
56.
57.
Monaghan JJ (2000) SPH without a tensile instability. J Comput Phys 159:290–311CrossRef
58.
Gray JP, Monaghan JJ, Swift RP (2001) SPH elastic dynamics. Comput Methods Appl Mech Eng 190:6641–6662CrossRef
59.
Fang J, Owens RG, Tacher L, Parriaux A (2006) A numerical study of the SPH method for simulating transient viscoelastic free surface flows. J Non-Newton Fluid Mech 139:68–84CrossRef
60.
Nestor RM, Basa M, Lastiwka M et al (2009) Extension of the finite volume particle method to viscous flow. J Comput Phys 228(5):1733–1749MathSciNetCrossRef
61.
Xu X, Ouyang J, Yang B, Liu Z (2013) SPH simulations of three-dimensional non-Newtonian free surface flows. Comput Methods Appl Mech Eng 256:101–116MathSciNetCrossRef
62.
Khayyer A, Gotoh H, Shimizu Y, Gotoh K (2016) Comparative study on accuracy and conservation properties of particle regularization schemes and proposal of an improved particle shifting scheme. In: Proceedings of the 11th international SPHERIC workshop, pp 416–423
63.
Marrone S, Colagrossi A, Le Touz’e D, Graziani G (2010) Fast free-surface detection and level-set function definition in SPH solvers. J Comput Phys 229:3652–3663CrossRef
64.
Randles PW, Libersky LD (1996) Smoothed particle hydrodynamics: some recent improvements and applications. Comput Methods Appl Mech Eng 139:375–408MathSciNetCrossRef
65.
Oishi CM, Martins FP, Tomé MF, Alves MA (2012) Numerical simulation of drop impact and jet buckling problems using the eXtended Pom–Pom model. J Non-Newton Fluid Mech 169:91–103CrossRef
66.
Keunings R (1986) On the high Weissenberg number problem. J Non-Newton Fluid Mech 20:209–226CrossRef
67.
Tanner RI (1970) A theory of die swell. J Polym Sci 8:2067–2078
68.
Crochet MJ, Keunings R (1982) Finite element analysis of die swell of a highly elastic fluid. J Non-Newton Fluid Mech 10:339–356CrossRef
69.
Tomé MF, Mangiavacchi N, Cuminato JA, Castelo A, McKee S (2002) A finite difference technique for simulating unsteady viscoelastic free surface flows. J Non-Newton Fluid Mech 106:61–106CrossRef
70.
Sadek SH, Yildiz M (2013) Modeling die swell of second-order fluids using smoothed particle hydrodynamics. J Fluids Eng 135:051103CrossRef
71.
Han C (ed) (2012) Multiphase flow in polymer processing. Elsevier, Amsterdam
Metadata
Title
A technique to remove the tensile instability in weakly compressible SPH
Authors
Xiaoyang Xu
Peng Yu
Publication date
12-01-2018
Publisher
Springer Berlin Heidelberg
Published in
Computational Mechanics / Issue 5/2018
Print ISSN: 0178-7675
Electronic ISSN: 1432-0924
DOI
https://doi.org/10.1007/s00466-018-1542-4

Other articles of this Issue 5/2018

Computational Mechanics 5/2018 Go to the issue

Original Paper

An adaptively refined XFEM with virtual node polygonal elements for dynamic crack problems

Original Paper

Influence of stochastic geometric imperfections on the load-carrying behaviour of thin-walled structures using constrained random fields

Original Paper

Lattice Boltzmann simulation of antiplane shear loading of a stationary crack

Original Paper

Application of an enriched FEM technique in thermo-mechanical contact problems

Original Paper

A smoothed finite element approach for computational fluid dynamics: applications to incompressible flows and fluid–structure interaction

Original Paper

An efficient hydro-mechanical model for coupled multi-porosity and discrete fracture porous media