Three-dimensional transient complex free surface flows: Numerical simulation of XPP fluid

► We solve numerically three-dimensional free surface flows of viscoelastic fluids. ► The non-Newtonian fluid is described by the eXtended Pom–Pom constitutive equation. ► The numerical scheme is constructed in the context of finite differences (MAC method). ► We present numerical results for the die swell problem and jet buckling phenomenon. In this paper we present a finite difference MAC-type approach for solving three-dimensional viscoelastic incompressible free surface flows governed by the eXtended Pom–Pom (XPP) model, considering a wide range of parameters. The numerical formulation presented in this work is an extension to three-dimensions of our implicit technique [Journal of Non-Newtonian Fluid Mechanics 166 (2011) 165–179] for solving two-dimensional viscoelastic free surface flows. To enhance the stability of the numerical method, we employ a combination of the projection method with an implicit technique for treating the pressure on the free surfaces. The differential constitutive equation of the fluid is solved using a second-order Runge–Kutta scheme. The numerical technique is validated by performing a mesh refinement study on a pipe flow, and the numerical results presented include the simulation of two complex viscoelastic free surface flows: extrudate-swell problem and jet buckling phenomenon.