Numerical Solution of the Upper-Convected Maxwell Model for Three-Dimensional Free Surface Flows (Communications in Computational Physics, 2018)
This work presents a finite difference technique for simulating three-dimensionalfree surface flows governed by the Upper-Convected Maxwell (UCM) constitutiveequation. A Marker-and-Cell approach is employed to represent the fluid free surfaceand formulations for calculating the non-Newtonian stress tensor on solid boundariesare developed. The complete free surface stress conditions are employed. Themomentum equation is solved by an implicit technique while the UCM constitutiveequation is integrated by the explicit Euler method. The resulting equations are solvedby the finite difference method on a 3D-staggered grid. By using an exact solution forfully developed flow inside a pipe, validation and convergence results are provided.Numerical results include the simulation of the transient extrudate swell and the comparisonbetween jet buckling of UCM and Newtonian fluids.