Dissipative particle dynamics with energy conservation: Isoenergetic integration and transport properties

Abstract

Simulations of nano-to micro-meter scale fluidic systems under thermal gradients require consistent mesoscopic methods accounting for both hydrodynamic interactions and proper transport of energy. One such method is dissipative particle dynamics with energy conservation (DPDE), which has been used for various fluid systems with non-uniform temperature distributions. Despite the success of the method, existing integration algorithms have shown to result in an undesired energy drift, putting into question whether the DPDE method properly captures properties of real fluids. We propose a modification of the velocity-Verlet algorithm with local energy conservation for each DPDE particle, such that the total energy is conserved up to machine precision. Furthermore, transport properties of a DPDE fluid are analyzed in detail. In particular, an analytical approximation for the thermal conductivity coefficient is derived, which allows the selection of a specific value a priori. Finally, we provide approximate expressions for the dimensionless Prandtl and Schmidt numbers, which characterize fluid transport properties and can be adjusted independently by a proper selection of model parameters, and therefore, made comparable with those of real fluids. In conclusion, our results strengthen the DPDE method as a very robust approach for the investigation of mesoscopic systems with temperature inhomogeneities. arXiv:1907.06186v1 [cond-mat.soft]

Transport coefficients from Einstein–Helfand relations using standard and energy-conserving dissipative particle dynamics methods

“…The thermal conductivity in non-equilibrium conditions was obtained as described in Section 3.1. In all cases, we also include the theoretical prediction derived from the superposition of the limit of interparticle heat transport dominance 37 and the limit of kinetic transport dominance, 44 i.e. ,We explored three cases.…”

“…The algorithm to update the position and momentum follows a velocity-Verlet integration scheme, while the energy is updated following a simple Euler form; see ref. 3, 5 and 38. For simplicity, we used the particle EoS given in eqn (44), in which the many-body potential u is independent of the particle temperature. All simulations were performed in reduced units, where r c is the unit of length, m is the unit of mass, and k B T is the unit of energy.…”

“…For the purposes of testing different conditions, we simulated: (a) systems with no conservative force, i.e., u( ỹ,n) = C V ỹ, cf. eqn (44), which is referred to as the ideal GenDPDE system, and (b) systems with a conservative force f C , obtained from a manybody force potential given by a quadratic well, i.e.,…”

Diffusiophoretic Brownian Dynamics: Characterization of Hydrodynamic Effects for an Active Chemoattractive Polymer

“…For later reference, we also introduce a variant of the Ph-BD method which takes into account an additional repulsive force F R among all monomers. We consider a finite-range soft repulsive force similar to those employed in DPD 79,80…”

“…For later reference, we also introduce a variant of the Ph-BD method which takes into account an additional repulsive force F R among all monomers. We consider a finite-range soft repulsive force similar to those employed in DPD , boldF R , i ( r i ) = prefix∑ j a i j [ 1 − r i j r c ′ ] boldr̂ i j normalΘ ( r i j − r c ′ ) Here, the strength of the repulsion a ij and the range of the interaction r c ′ are parameters that can be varied according to the model requirements.…”