Liquid jet break-up appears in many technical applications, as well as in nature. It consists of complex physical processes, which happen on very small scales in space and time. This makes them hard to capture by experimental methods; and therefore a prime subject for numerical investigations. The state-of-the-art approach combines the Volume of Fluid (VOF) method with Direct Numerical Simulations (DNS) as employed in the ITLR in-house code Free Surface 3D (FS3D). The simulation of these jets is dependent on very fine grids, with most of the computational costs incurred by solving the Pressure Poisson Equation. In order to simulate larger computational domains, we tried to improve the performance of FS3D by the implementation of a new multigrid solver. For this we selected the solver contained in the UG4 package developed by the Goethe Center for Scientific Computing at the University of Frankfurt. We will show simulations of the primary break-up of shear-thinning liquid jets and explain why larger computational domains are necessary. Results are preliminary. We demonstrate that the implementation of UG4 into FS3D provides a noticeable increase in weak scaling performance, while the change in strong scaling is yet detrimental. We will then discuss ways to further improve these results.