A numerical study of strongly overdamped Dissipative Particle Dynamics (DPD) systems

In this paper, we investigate the behaviour of a Dissipative Particle Dynamics (DPD) system in the overdamped limit where the particles approach zero mass limit. In this limit, the DPD system becomes singular. We propose two numerical schemes to deal with this system - one results in a fully-populated but well-conditioned matrix system, while the other employs a deflation technique to handle the system in an iterative manner, where the eigenvalue of −1 corresponding to a rigid-body motion is mapped to zero. The latter iterative scheme is to be preferred, with the possibility of parallel implementations. Some numerical results are presented to verify the two proposed schemes.