COMPARISON OF COMPUTATIONAL-EFFICIENCY OF FLOW SIMULATIONS WITH MULTIMODE CONSTITUTIVE-EQUATIONS - INTEGRAL AND DIFFERENTIAL MODELS

A decoupled finite-element method (INT/FEM) is presented for calculati on of two-dimensional viscoelastic flows with integral constitutive mo dels. The momentum and continuity equations are solved by Galerkin's m ethod with the viscoelastic stress treated as a fixed body force. The viscoelastic stress is computed by using the stream function to track fluid particles upstream, integrating a system of ordinary differentia l equations that govern the displacement-gradient tensor, and evaluati ng the integral constitutive equation by numerical quadrature. The qua si-linear upper-convected Maxwell and Oldroyd-B models, as well as the nonlinear model of Papanastasiou, Scriven and Macosko (PSM), are used in the simulations. The efficiency of the integral method is compared to that of the recently developed finite-element method (EVSS/FEM) fo r differential constitutive models. Convergence and accuracy of the IN T/FEM are shown by calculations for flow between eccentric cylinders. The upper limit in De attainable by using the INT/FEM is comparable to values for the EVSS/FEM only for constitutive models with a shear-thi nning ratio of the first normal stress difference to the shear stress and a large solvent contribution to the solution viscosity. The INT/FE M becomes the more efficient technique for simulation with this type o f constitutive equation When three or more relaxation modes are includ ed in the memory function.