Multiscale modeling of viscoelastic fluids: an up-to-date CONNFFESSIT

Abstract

The present communication introduces an up-to-date version of the CONNFFESSIT method in the field of micro-macro simulations of non-Newtonian fluids. The ‘macro’ section employs a semi-Lagrangian method in order to reduce the Navier-Stokes equations to a Stokes-like subproblem. Linear systems arising from the finite element formulation are solved via the ‘Incomplete Cholesky Conjugate Gradient’ iterative algorithm, wherein the sparsity pattern of the matrices is taking into account. As to the ‘micro’ part, the stochastic formulation simplifies the Fokker-Planck equations in the configuration space to stochastic differential equations for the internal degrees of freedom of the particles (‘dumbbells’) conveying the rheological information of the kinetic model, their integration being accomplished by means of a semi-implicit, PredictorCorrector algorithm. The ‘micro-macro’ coupling involves the polymer stress tensor, which is computed through a mixed ‘Finite Element / Natural Element’ method.An extended, search-and-locate method for unstructured meshes and non-connected domains has been implemented. The robustness and efficiency of the method is highlighted on a benchmark problem (10:1 planar contraction).