A method for multiscale simulation of flowing complex fluids

Abstract

The Brownian configuration fields (BCF) method provides an attractive approach to simultaneous solution of flow and microstructure problems in complex fluids. At the continuum level, it is implemented in an Eulerian reference frame (i.e. on a stationary computational mesh), which makes it amenable to standard computational approaches for convection problems, and at the microstructural level it simply involves adding a convective term to the evolution of individual Brownian dynamics trajectories. We present here a variation on BCF that may hold advantages over the original formulation. It uses a hybrid representation of the configurational distribution function (CDF), splitting a time step into two parts: (1) a standard Brownian dynamics step (here the CDF is implicitly represented as a superposition of delta-functions) and (2) a convective step, where the distribution is projected onto an orthogonal polynomial basis and convection problems are solved for the generalized Fourier coefficients, then “lifted” back to the delta-function basis. This approach, which we call operator-splitting coefficient-matching (OSCM) allows the solution of fewer convection problems per time step than BCF and guarantees spatial smoothness of the convected properties—in some sense it is a filtered version of BCF. We present comparisons of accuracy and computational efficiency of BCF and OSCM for a simple model problem involving bead-spring dumbbells and chains. The efficiency of the two methods is comparable, and in situations where the finite extensibility becomes important, BCF can lose accuracy, due to a loss of correlation between trajectories at different point in the flow domain, where OSCM does not.