Towards shape optimization of profile extrusion dies with respect to homogeneous die swell

► Shape optimization of profile extrusion dies with respect to homogenous die swell. ► Use of Oldroyd-B and Giesekus models to represent the viscoelastic behavior. ► New Galerkin/Least-Squares stabilization parameter for the constitutive equation. ► 2D shape optimization test case comparing the influence of the material model on the optimization outcome. ► NURBS representation for free surface flows as an addition to classical interface tracking