NUMERICAL SOLUTION OF THE GIESEKUS MODEL FOR TWO-DIMENSIONAL FLOWS

Araujo, Matheus Tozo¹; Tomé, Murilo Francisco¹

¹ ICMC-USP - BRAZIL

doi:10.20906/CPS/COB-2015-0961

Resumo

This work has the objective to present a numerical method to simulate two-dimensional viscoelastic free surface flows governed by the Giesekus constitutive equation (J. Non-Newt. Fluid Mech., 40 (1991), 79-102). The governing equations are solved by the finite difference method on a staggered grid. The calculation of velocity and pressure is performed by an implicit method of second order in space and first order in time, while the Giesekus constitutive equation is solved by a second-order Runge-Kutta method. To verify the proposed numerical method, the authors develop an analytic solution for the steady flow of a Giesekus fluid between two parallel plates. Convergence results are provided by the use of mesh refinement.

Palavras-chave: Finite difference; Viscoelastic flows; Analytic solution; Giesekus model