A numerical framework to simulate dispensing of fluids with different types of complex rheology is presented. The framework is based on an incompressible flow solver that uses immersed boundary methods and an automatically generated octree grid. It therefore supports simulation with arbitrary geometry and of moving application with various injection models with minimum setup time. The framework also supports rheology models spanning from purely viscous models to more advanced viscoelastic stress models. Three examples of applications are given, namely for seam sealing in automotive bodies, swirled adhesive extrusion and wire fed additive manufacturing of metal. The wide range of applications shows the potential of the framework and indicates that many more possible applications are conceivable.