Colloidal suspension by SRD–MD simulation on GPU

Abstract

In this paper, we focus on a coarse-grained model for fluid simulation named Stochastic Rotation Dynamics (SRD) combined with colloids simulated with Molecular Dynamics (MD). In this method, the fluid is represented by point particles with continuous velocities distributed in small cells. The coupling between the dynamics of the fluid particles and the dynamics of colloids is performed by applying repulsive forces between these two kinds of particles at each MD step. As this method is computationally expensive for large systems, we propose an approach adapted to graphical processing units (GPU) that outperforms existing methods by associating each colloid to a block of parallel threads. This strategy offers a better workload balance on the GPU even for systems with a large number of neighbors.

Introduction

During the last few decades, numerous computer simulations have been developed to study soft matter (including complex fluids, polymers in suspension, colloidal suspensions, etc.). In this field, “large” particles are studied taking into account thermal fluctuations, which need specific simulations. Brownian dynamics simulations (BD) [1], dissipative particles dynamics simulations (DPD) [2] or Lattice-Boltzmann simulations (LB) [[3], [4]] are among the common methods used for these studies. In BD, the fluid is modeled as a continuum medium although in the two other methods, it is described by a coarse-grained model. In this paper, we focus on another kind of simulation using a coarse-grained model for the fluid particles, namely stochastic rotation dynamics (SRD) also known as multi-particle collision dynamics (MPCD), which was first introduced by Malevanets and Kapral in 1999 [[5], [6]]. Many applications and variants of this method have been extensively reviewed in Refs. [7] and [8]. In this method, the fluid is represented by point particles with continuous positions and velocities distributed in small cells. The dynamics of the fluid proceeds in two steps: a streaming step and a collision step. During the streaming step, the fluid particles move ballistically according to their velocity and during the collision step, a stochastic rotation of the relative velocity of each particle in each cell is applied. The dynamics of fluid particles is thus described without calculating any explicit interactions between them. When embedded colloids are introduced in the system, their dynamics is described by a traditional molecular dynamics scheme (MD) and simulations are called hybrid SRD–MD simulations. In order for the fluid and the colloids to interact, the SRD simulation of the fluid has to be coupled with the MD simulation of the colloids. Different coupling methods exist in the literature. The most common and the simplest one is to introduce the colloids in the collision step of the fluid. In this manner, only the colloid–colloid interactions are explicitly calculated. The exchange of momentum between fluid particles and colloids takes place in the collision steps of SRD. This coupling was largely applied and give good results when the colloids concentration is moderate [9]. It is also very suitable for parallelization and a GPU version has recently been developed by Westphal et al. [10]. However because of its simplicity, it fails to model precisely the hydrodynamics. The fluid can penetrate inside the colloids, therefore this method cannot describe the lubrication effects. In this paper, another coupling is considered. It consists in introducing explicit repulsive interactions between the colloids and the fluid particles, which are chosen to avoid depletion and to mimic the lubrication [11]. In this method called in the following ‘SRD–MD with force coupling’, the fluid particles are not allowed to penetrate deeply into the colloids and thus, they are not homogeneously distributed in the simulation box. The main disadvantage is that, as more interactions must be computed for each MD step, this method becomes computationally expensive for large systems. To improve the performance of such kind of simulations, we propose here a code suitable for graphical processing units (GPU) calculations.

This paper is organized as follows. First, in Section 2, the hybrid SRD–MD simulations are described. Then, the GPU implementation details are presented in Section 3. Finally, Section 4 summarizes our results.