Brownian Configuration Fields Research Articles

Adaptive configuration fields: a new multiscale simulation technique for reptation-based models with a stochastic strain measure and local variations of life span distribution

In this work a new multiscale simulation technique, i.e. Adaptive configuration fields method (ACFM), has been proposed for complex flow simulation of state-of-the-art reptation-based models for entangled polymeric systems. Specifically, this technique combines the essential aspects of the previously introduced Brownian configuration fields and the deformation fields methods [J. Non-Newtonian Fluid Mech. 70 (1997) 79; J. Non-Newtonian Fluid Mech. 89 (2000) 209] to allow simulation of advanced reptation models with a stochastic strain measure and local variations of life span distribution. In order to examine the fidelity and robustness of our new simulation technique, we have performed simulations in a number of different fixed kinematics flows using the single segment reptation model of Öttinger [J. Rheol. 44 (2000) 1293], which possesses the essential features required for quantitatively describing the non-linear rheology of polymer melts, but cannot be implemented in a complex flow using the available state-of-the-art Eulerian multiscale simulation techniques, namely, the Brownian configuration fields or the deformation fields. In turn, the simulation results in unidirectional flows are compared with pure Brownian dynamics simulations and it is shown that the results are in excellent agreement, thus verifying the accuracy of the adaptive configuration fields method.

Convergence of a Stochastic Method for the Modeling of Polymeric Fluids

We present a convergence analysis of a stochastic method for numerical modeling of complex fluids using Brownian configuration fields (BCF) for shear flows. The analysis takes into account the special structure of the stochastic partial differential equations for shear flows. We establish the optimal rate of convergence. We also analyze the nature of the error by providing its leading order asymptotics.

Brownian configuration fields and variance reduced CONNFFESSIT

Stochastic simulation techniques, such as Brownian dynamics, provide us an extremely powerful tool for solving the usually nonlinear equations describing polymer dynamics in solutions and melts [1]. However, the most challenging problems (e.g. the investigation of the universal behaviour of long polymer chains, or the flow calculation based on stochastic simulation techniques) involve a very large number of degrees of freedom and hence require an enomous amount of computer time. In order to solve such problems on currently available computers it is therefore necessary to develop strategies to drastically suppress the level of the fluctuations in the simulations. The purpose of this note is to show that the recently proposed concept of Brownian configuration fields [2] in viscoelastic flow calculations can be regarded as an extremely powerful extension of variance reduction techniques based on parallel process simulation.