Wavelet Monte Carlo dynamics: A new algorithm for simulating the hydrodynamics of interacting Brownian particles

Abstract

We develop a new algorithm for the Brownian dynamics of soft matter systems that evolves time by spatially correlated Monte Carlo moves. The algorithm uses vector wavelets as its basic moves and produces hydrodynamics in the low Reynolds number regime propagated according to the Oseen tensor. When small moves are removed, the correlations closely approximate the Rotne-Prager tensor, itself widely used to correct for deficiencies in Oseen. We also include plane wave moves to provide the longest range correlations, which we detail for both infinite and periodic systems. The computational cost of the algorithm scales competitively with the number of particles simulated, N, scaling as N ln N in homogeneous systems and as N in dilute systems. In comparisons to established lattice Boltzmann and Brownian dynamics algorithms, the wavelet method was found to be only a factor of order 1 times more expensive than the cheaper lattice Boltzmann algorithm in marginally semidilute simulations, while it is significantly faster than both algorithms at large N in dilute simulations. We also validate the algorithm by checking that it reproduces the correct dynamics and equilibrium properties of simple single polymer systems, as well as verifying the effect of periodicity on the mobility tensor.

Universal dynamics of dilute and semidilute solutions of flexible linear polymers

“…This is because they require the incorporation of hydrodynamic interactions, which is challenging within the framework of methodologies conventionally used to simulate static properties. Recently, however, there has been significant progress in the development of simulation algorithms that account for hydrodynamic interactions, and they have been used to predict both dynamic properties at equilibrium and far-from-equilibrium rheological properties [6,[14][15][16][17][18][19][20][21][22]. In this review I will discuss attempts in the past few years at applying these new algorithms to investigate the universal aspects of the dynamics of polymer solutions.…”

Influence of thermal fluctuations on active diffusion at large Péclet numbers

“…The mobility tensors used in this work are those that appear in Wavelet Monte Carlo Dynamics (WMCD) 37,38 , described below, which smoothly bridge the large r and δ ij terms.…”

“…Another reason for the limited microswimmer work including thermal fluctuations is the great computational expense required to include the correct hydrodynamics of thermal fluctuations, which is a challenge well known to the polymer community where it has spawned a wide range of simulation algorithms [35][36][37] . Here we make use of the recently developed Wavelet Monte Carlo dynamics (WMCD) algorithm to include hydrodynamically coupled thermal fluctuations efficiently 37,38 .…”

Universal scaling and characterisation of gelation in associative polymer solutions

“…Accounting for hydrodynamic interactions in the semidilute regime of concentration, on the other hand, is challenging since both intra and intermolecular interactions need to be taken into consider-ation, particularly in the case of the latter since hydrodynamic interactions are long-ranged in space. Significant advances have been made over the last decade in our capacity to simulate semidilute polymer solutions due to the development of a variety of mesoscopic simulation techniques based on coarse-grained bead-spring chain models for polymer molecules [52][53][54][55][56][57][58][59][60][61][62][63]. These algorithms are able to describe long polymers that overlap with each other while maintaining a low segment density, and are also able to capture the interaction of segments with each other through solvent-mediated hydrodynamic interactions.…”