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Session Chair: Sven Klinkel, RWTH Aachen Universtity Session Chair: Alexander Düster, Hamburg University of Technology
Location:Auditorium Wolfsburg
Presentations
A Space-Time Galerkin/ Least Squares finite element method for the three-field viscoelastic flows
Stylianos Varchanis1, Pantelis Moschopoulos2, Yiannis Dimakopoulos2, John Tsamopoulos2
1Micro/Bio/Nanouidics Unit, Okinawa Institute of Science and Technology, Onna, Okinawa 904-0495, Japan; 2Laboratory of Fluid Mechanics and Rheology, Department of Chemical Engineering, University of Patras, Greece
Initially, the Space-Time Galerkin/ Least-Squares (ST-GLS) finite element method was proposed to solve the equations of motion for incompressible or compressible Newtonian fluids [1-2]. Based on the ST- GLS principle, we present a new, fully consistent and highly stable finite element method for non-Newtonian fluid flows, specifically designed for the three-field incompressible viscoelastic flows. Space and time are discretized using finite elements and all flow variables (velocity-pressure-stresses) are interpolated with polynomials of the same degree. The positive definiteness of the conformation tensor, which encapsulates the deformation history of the polymeric fluid, is enforced by a square-root reformulation of the constitutive equation [3]. The method is enriched with a consistent shock-capturing scheme that suppresses numerical oscillations around stress singularities. Multiphase flows are treated by coupling the present formulation with a quasi-elliptic mesh generator [4], providing accurate descriptions of interfacial dynamics. The accuracy, robustness, and generality of the method are validated in stationary and transient benchmark flows of viscoelastic fluids. We consider the creeping flow of an Oldroyd-B fluid past a cylinder in a straight channel. We then proceed to the axisymmetric capillary thinning of viscoelastic filament in which the bead-on-a-string formation appears. Finally, we present for the first time the symmetry breaking in 3-dimensional viscoelastic simulations of a falling sphere or a rising bubble. In all cases, we obtain numerically stable solutions for very high values of the Weissenberg number, which is defined as the shear rate times the relaxation time of the polymeric fluid and represents the importance of elastic effects over shear ones,that have never been accessed before by existing numerical methods.
References
[1] T. J. R. Hughes, L. P. Franca, G. M. Hulbert, Comp. meth. App. Mech. Eng., 73 (1989).
[2] T. E. Tezduyar, Advances in applied mechanics 28 (1991).
[3] N. Balci, B. Thomases, M. Renardy, C. R. Doering, J. Non-Newt. Fluid Mech., 166 (2011).
[4] Y. Dimakopoulos, J. Tsamopoulos, JCP, 192 (2003)
