Summary
The method of smoothed dissipative particle dynamics (SDPD) is a novel coarse grained method for simulation of complex fluids. It has some advantages over more traditional particles based methods (Espanol and Warren, Europhys. Lett. 30(4):191–196, 1995). But one of the problems common for particle based simulations of microfluid system takes place also for SDPD: it fails to realize Schmidt number of O(103) typical of liquids.
In present paper we apply the implicit numerical scheme that allows significantly increase time step in SDPD and perform simulation for larger Schmidt number. Simulations using this methods show close agreement with serial solutions for Couette and Poiseuille flows. The results of benchmarks based on temperature control are presented. The dependence of self-diffusion coefficient D on kinematic viscosity is examined and found to be in agreement with empirical observations (Li and Chang, J. Chem. Phys. 23(3):518–520, 1955).
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Espanol P, Warren P (1995) Statistical mechanics of dissipative particle dynamics. Europhys Lett 30(4):191–196
Li J, Chang J (1955) Self-diffusion coefficient and viscosity in liquids. J Chem Phys 23(3):518–520
Monaghan JJ (2005) Smoothed particle hydrodynamics. Rep Prog Phys 68:1703–1759
Espanol P, Revenga M (2003) Smoothed dissipative particle dynamics. Phys Rev E 67:026705
Groot RD, Warren PB (1997) Dissipative particle dynamics: Bridging the gap between atomistic and mesoscopic simulation. J Chem Phys 107:4423–4435
Jiang WH, Huang JH, Wang YM, Laradji M (2007) Hydrodynamic interaction in polymer solutions simulated with dissipative particle dynamics. J Chem Phys 126:044901
Symeonidis V, Karniadakis GE, Caswell B (2005) Dissipative particle dynamics simulations of polymer chains: Scaling laws and shearing response compared to dna experiments. Phys Rev Lett 95:076001
Symeonidis V, Karniadakis GE (2006) A family of time-staggered schemes for integrating hybrid dpd models for polymers: Algorithms and applications. J Comput Phys 218:82–101
Shardlow T (2003) Splitting for dissipative particle dynamics. SIAM J Sci Comput 24(4):1267–1282
Monaghan J (1997) Implicit sph drag and dusty gas dynamics. J Comput Phys 138(2):801–820
Hu X, Adams N (2006) A multi-phase sph method for macroscopic and mesoscopic flows. J Comput Phys 213:844–861
Hu XY, Adams NA (2006) Angular-momentum conservative smoothed particle dynamics for incompressible viscous flows. Phys Fluids 18:101702
Grmela M, Öttinger H (1997) Dynamics and thermodynamics of complex fluids. I. development of a general formalism. Phys Rev E 56(6):6620–6632
Öttinger H, Grmela M (1997) Dynamics and thermodynamics of complex fluids. II. Illustrations of a general formalism. Phys Rev E 56(6):6633–6655
Serrano M, Español P (2001) Thermodynamically consistent mesoscopic fluid particle model. Phys Rev E 64(4):46115
Morris JP, Fox PJ, Zhu Y (1997) Modeling low Reynolds number incompressible flows using sph. J Comput Phys 136:214–226
Pagonabarraga I, Hagen M, Frenkel D (1998) Self-consistent dissipative particle dynamics algorithm. Europhys Lett 42(4):377–382
Nikunen P, Karttunen M, Vattulainen I (2003) How would you integrate the equations of motion in dissipative particle dynamics simulations? Comput Phys Commun 153:407–423
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer Science + Business Media B.V.
About this paper
Cite this paper
Litvinov, S., Hu, X.Y., Adams, N.A. (2009). Splitting for Highly Dissipative Smoothed Particle Dynamics. In: Ellero, M., Hu, X., Fröhlich, J., Adams, N. (eds) IUTAM Symposium on Advances in Micro- and Nanofluidics. IUTAM Bookseries, vol 15. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-2626-2_16
Download citation
DOI: https://doi.org/10.1007/978-90-481-2626-2_16
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-2625-5
Online ISBN: 978-90-481-2626-2
eBook Packages: EngineeringEngineering (R0)