Size reduction methods for the implicit time-dependent simulation of micro–macro viscoelastic flow problems

Traditionally, micro–macro simulations have been performed using simple explicit time-marching algorithms, which lack the desirable stability of implicit methods. In this study, a fully implicit time integration scheme is presented and implemented for the first time for the solution of time-dependent complex flows using the Brownian Configuration Fields approach. Special techniques need to be applied to deal with the very large size of the resulting linear systems. A novel size-reduction scheme is used, allowing an independent treatment for each molecular field and suited to parallel hardware architecture. To illustrate the method, a selected number of applications using linear spring chains are presented and the results are compared with their corresponding closed form constitutive equation. The excellent agreement between the results demonstrates the feasibility of the proposed approach.