Abstract
Materials like fluids are long since important research objects of continuum mechanics as well as of computer graphics. Smoothed particle hydrodynamics(SPH) is one of the representation methods employed for continuous materials. Its simplicity in implementation and its realistic representation are drastically improved during the last decades. More recently, highly viscous fluids like honey, jam, and bread dough based on the SPH formulation have gained attention with impressive results. In this chapter, a novel implicit viscosity method is proposed. The internal viscosity forces are recursively calculated from the difference of the nearby velocities of the particles until they are small enough to be neglected. The proposed approach has longer time-steps compared with existing explicit viscosity methods, resulting in shorter computation time. Besides, the proposed method uses a physical viscosity coefficient, not an artificial one like in existing implicit viscosity methods, which helps predict the viscous behavior of continuous materials more accurately. The obtained results show that the computational time for the proposed approach is predictable, while the accuracy in modelling the viscosity behaviour is similar or higher than existing methods.
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References
T.J. Chung. Computational Fluid Dynamics (Cambridge University Press, 2010)
R. Eymard, T. Gallouët, R. Herbin, Finite volume methods. Handb. Numer. Anal. 7, 713–1018 (2000)
G. Irving, J. Teran, R. Fedkiw, Invertible finite elements for robust simulation of large deformation, in 2004 ACM SIGGRAPH/Eurographics Symposium on Computer Animation, pp. 131–140 (2004)
O.C. Zienkiewicz, R.L. Taylor, J.Z. Zhu. The Finite Element Method Set (Butterworth-Heinemann, 2005)
G.R. Liu, J. Zhang, K.Y. Lam, H. Li, G. Xu, Z.H. Zhong, G.Y. Li, X. Han, A gradient smoothing method (GSM) with directional correction for solid mechanics problems. Comput. Mech. 41(3), 457–472 (2008)
M.B. Liu, G.R. Liu, Smoothed Particle Hydrodynamics (SPH): an overview and recent developments. Arch. Comput. Methods Eng. 17(1), 25–76 (2010)
J.J. Monaghan, Smoothed particle hydrodynamics. Rep. Prog. Phys. 68(1), 1703–1759 (2005)
J.U. Brackbill, H.M. Ruppel, FLIP: A method for adaptively zoned, particle-in-cell calculations of fluid flows in two dimensions. J. Comput. Phys. 65(2), 314–343 (1986)
J. Cornelis, M. Ihmsen, A. Peer, M. Teschner, IISPH-FLIP for incompressible fluids. Comput. Gr. Forum 33(2), 255–262 (2014)
A. Stomakhin, C. Schroeder, L. Chai, J. Teran, A. Selle, A material point method for snow simulation. ACM Trans. Gr. 32(4), 102:1–102:10 (2013)
D. Sulsky, S.-J. Zhou, H.L. Schreyer, Application of a particle-in-cell method to solid mechanics. Comput. Phys. Commun. 87(1), 236–252 (1995)
M. Macklin, M. Müller, Position based fluids. ACM Trans. Graph. 32(4), 104:1–104:12 (2013)
M. Müller, B. Heidelberger, M. Hennix, J. Ratcliff, Position based dynamics. J. Vis. Commun. Image Represent. 18(2), 109–118 (2007)
F.H. Harlow, The particle-in-cell method for numerical solution of problems in fluid dynamics Los Alamos Scientific Lab., N. Mex, Technical report (1962)
Y. Zhu, R. Bridson, Animating sand as a fluid. ACM Trans. Gr. 24(3), 965–972 (2005)
T. Takahashi, Y. Dobashi, I. Fujishiro, T. Nishita, Volume preserving viscoelastic fluids with large deformations using position-based velocity corrections. Vis. Comput. 32(1), 57–66 (2016)
R.A. Gingold, J.J. Monaghan, Smoothed particle hydrodynamics-theory and application to non-spherical stars. Mon. Not. R. Astron. Soc. 181, 375–389 (1977)
L.B. Lucy, A numerical approach to the testing of the fission hypothesis. Astron. J. 82, 1013–1024 (1977)
J.J. Monaghan, R.A. Gingold, Shock simulation by the particle method SPH. J. Comput. Phys. 52(2), 374–389 (1983)
J.J. Monaghan, Smoothed particle hydrodynamics. Ann. Rev. Astron. Astrophys. 30(1), 543–574 (1992)
J.J. Monaghan, Simulating free surface flows with SPH. J. Comput. Phys. 110(2), 399–406 (1994)
M. Desbrun, M.-P. Gascuel, Smoothed particles: A new paradigm for animating highly deformable bodies, in Eurographics Workshop on Computer Animation and Simulation ’96, pp. 61–76 (1996)
S.J. Cummins, M. Rudman, An SPH projection method. J. Comput. Phys. 152(2), 584–607 (1999)
S. Shao, E.Y.M. Lo, Incompressible SPH method for simulating Newtonian and non-Newtonian flows with a free surface. Adv. Water Res. 26(7), 787–800 (2003)
M. Becker, M. Teschner, Weakly compressible SPH for free surface flows, in 2007 ACM SIGGRAPH/Eurographics Symposium on Computer Animation, pp. 209–217 (2007)
B. Solenthaler, R. Pajarola, Predictive-corrective incompressible SPH. ACM Trans. Gr..s, 28(3), 40:1–40:6 (2009)
B. Solenthaler, R. Pajarola, Predictive-corrective incompressible SPH, in ACM SIGGRAPH 2009 Papers, pp. 40:1–40:6 (2009)
M. Ihmsen, J. Cornelis, B. Solenthaler, C. Horvath, M. Teschner, Implicit incompressible SPH. IEEE Trans. Vis. Comput. Gr. 20(3), 426–435 (2014)
J. Bender, D. Koschier, Divergence-free smoothed particle hydrodynamics, in 14th ACM SIGGRAPH/Eurographics Symposium on Computer Animation, pp. 147–155 (2015)
J.P. Morris, P.J. Fox, Y. Zhu, Modeling low Reynolds number incompressible flows using SPH. J. Comput. Phys. 136(1), 214–226 (1997)
S. Clavet, P. Beaudoin, P. Poulin, Particle-based viscoelastic fluid simulation, in 2005 ACM SIGGRAPH/Eurographics Symposium on Computer Animation, pp. 219–228 (2005)
Y. Chang, K. Bao, J. Zhu, E. Wu, High viscosity fluid simulation using particle-based method, in 2011 IEEE International Symposium on VR Innovation, pp. 199–205 (2011)
M. Müller, D. Charypar, M. Gross, Particle-based fluid simulation for interactive applications, in ACM Eurographics/SIGGRAPH Symposium on Computer Animation, pp. 154–159 (2003)
M.M. Cross, Rheology of non-Newtonian fluids: A new flow equation for pseudoplastic systems. J. Colloid Sci. 20, 417–437 (1965)
L.F.d.S. Andrade, M. Sandim, F. Petronetto, P. Pagliosa, A. Paiva, SPH fluids for viscous jet buckling, in 27th SIBGRAPI Conference on Graphics, Patterns and Images, pp. 65–72 (2014)
L.F.d.S. Andrade, M. Sandim, F. Petronetto, P. Pagliosa, A. Paiva. Particle-based fluids for viscous jet buckling. Comput. Gr. 52, 106–115 (2015)
T. Takahashi, Y. Dobashi, I. Fujishiro, T. Nishita, M.C. Lin, Implicit formulation for SPH-based viscous fluids. Comput. Gr. Forum 34(2), 493–502 (2015)
A. Peer, M. Ihmsen, J. Cornelis, M. Teschner, An implicit viscosity formulation for SPH fluids. ACM Trans. Gr. 34(4), 114:1–114:10 (2015)
J. Bender, D. Koschier, Divergence-free SPH for incompressible and viscous fluids. IEEE Trans. Visual Comput. Gr. 23, 1193–1206 (2017)
H. Barreiro, I. García-Fernández, I. Alduán, M.A. Otaduy, Conformation constraints for efficient viscoelastic fluid simulation. ACM Trans. Gr. 36(6), 221:1–221:11 (2017)
M. Weiler, D. Koschier, M. Brand, J. Bender, A physically consistent implicit viscosity solver for SPH fluids. Comput. Gr. Forum 37(2), 145–155 (2018)
M. Carlson, P.J. Mucha, R.B. Van Horn III, G. Turk, Melting and flowing, in 2002 ACM SIGGRAPH/Eurographics Symposium on Computer Animation, pp. 167–174 (2002)
C. Batty, R. Bridson, Accurate viscous free surfaces for buckling, coiling, and rotating liquids, in 2008 ACM SIGGRAPH/Eurographics Symposium on Computer Animation, pp. 219–228 (2008)
A. Peer, M. Ihmsen, Prescribed velocity gradients for highly viscous SPH fluids with vorticity diffusion. IEEE Trans. Visual Comput. Gr. 23(12), 2656–2662 (2016)
E. Rossi, A. Colagrossi, D. Durante, G. Graziani, Simulating 2D viscous flow around geometries with vertices through the diffused vortex hydrodynamics method. Comput. Methods Appl. Mech. Eng. 302, 147–169 (2016)
A.E. Chorin. A Mathematical Introduction to Fluid Mechanics (Springer, 1992)
A. Powell, MIT materials science and engineering. 3.21 Lectures on Fluid Flow and Kinectics (2003)
R. Temam, Navier-Stokes Equations: Theory and Numerical Analysis (AMS Chelsea Publishing, 1977)
M. Ihmsen, J. Orthmann, B. Solenthaler, A. Kolb, M. Teschner, SPH fluids in computer graphics, in EUROGRAPHICS 2014 — State of The Art Report, pp. 21–42 (2014)
M. Kelager, Lagrangian fluid dynamics using smoothed particle hydrodynamics. Master’s thesis, University of Copenhagen (2006)
M. Gomez-Gesteira, B.D. Rogers, R.A. Dalrymple, A. Crespo, State-of-the-art of classical SPH for free-surface flows. J. Hydraul. Res. 48, 6–27 (2010)
F. Colin, R. Egli, F.Y. Lin, Computing a null divergence velocity field using smoothed particle hydrodynamics. J. Comput. Phys. 217(2), 680–692 (2006)
H.-S. Dou, B. Khoo, Investigation of turbulent transition in plane Couette flows using energy gradient method. Adv. Appl. Math. Mech. 3, 165–180 (2005)
X. X, J. Ouyang, W. Li, Q. Liu, SPH simulations of 2D transient viscoelastic flows using brownian configuration fields. J. Non-Newtonian Fluid Mech. 208, 59–71 (2014)
L. Trefethen, A.E. Trefethen, S.C. Reddy, T. Driscoll, Hydrodynamic stability without eigenvalues. Science 261(5121), 578–584 (1993)
E. Mitsoulis, Numerical simulation of calendering viscoplastic fluids. J. Nonnewton. Fluid Mech. 154(2–3), 77–88 (2008)
E. Mitsoulis, S.G. Hatzikiriakos, Rolling of bread dough: Experiments and simulations. Food Bioprod. Process. 87(2), 124–138 (2009)
S. Sofou, E.B. Muliawan, S.G. Hatzikiriakos, E. Mitsoulis, Rheological characterization and constitutive modeling of bread dough. Rheol. Acta 47(4), 369–381 (2008)
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Kim, JT., Ruggiero, F., Lippiello, V., Siciliano, B. (2022). Smoothed Particle Hydrodynamics-Based Viscous Deformable Object Modelling. In: Siciliano, B., Ruggiero, F. (eds) Robot Dynamic Manipulation. Springer Tracts in Advanced Robotics, vol 144. Springer, Cham. https://doi.org/10.1007/978-3-030-93290-9_3
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DOI: https://doi.org/10.1007/978-3-030-93290-9_3
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