Fluid Particle Dynamics: A Synthesis of Dissipative Particle Dynamics and Smoothed Particle Dynamics

Fluid particle dynamics: a synthesis of dissipative particle dynamics and smoothed particle dynamics Pep Espa~ nol() (received ; accepted) PACS. 47.11+j { Computational methods in uid mechanics. Abstract. { We present a generalization of dissipative particle dynamics that includes shear forces between particles. The new algorithm has the same structure as the (isothermal) smoothed particle dynamics algorithm, except that it conserves angular momentum and includes thermal uctuations consistently with the principles of equilibrium statistical mechanics. This clariies the connection of dissipative particle dynamics with numerical resolution algorithms of the macroscopic Navier-Stokes equations. The modelization of complex uids like colloidal and polymeric suspensions, microemulsions, immiscible uids, etc. requires the simultaneous consideration of the macroscopic and meso-scopic aspects of hydrodynamics. The former is responsible, for example, for the hydrodynamic many-body interactions between suspended objects whereas the mesoscopic aspects account for the uctuations that cause Brownian diiusion. In recent years, techniques such as lattice gas or lattice Boltzmann have been deviced in order to address both aspects of hydrodynamics in complex uids 1]. However, the presence of a lattice has certain disatvantages as, for example, the lack of Galilean invariance, the complexity of look-up tables in three dimensions or the cumbersome treatment of boundaries on shaped bodies. Another recent technique introduced by Hoogerbrugge and Koelman 2, 3] is dissipative particle dynamics (DPD). DPD is an oo-lattice simulation technique which is particularly exible for modeling and appears as a serious competitor to the mentioned techniques. The technique has received substantial theoretical support 4, 5] and it has been successfully applied in a large variety of systems including ow in porous media 3], colloidal suspension 3, 6], dilute polymeric suspensions 7], and immiscible binary uids 8]. The idea behind DPD is to simulate a Newtonian uid (as, for example, the Newtonian solvent in colloidal or polymeric suspensions) in terms of mesoscopic \lumps" or \droplets" of uid, named dissipative particles 2, 9]. It is postulated that these dissipative particles interact with each other with a pair-wise conservative potential, with dissipative forces that depend