Numerical simulation of 2D unsteady shear-thinning non-Newtonian incompressible fluid in screw extruder with fictitious domain method

In this paper, we develop a fictitious domain method with Distributed Lagrange Multipliers for simulating 2D unsteady shear-thinning non-newtonian incompressible flow in a single-screw and twin-screw extruder. The advantage of the fictitious domain method is that one can use a fixed mesh even as the fluid domain changes in time (as the screws are rotating), eliminating the need for repeated remeshing and projection. The method uses a finite element discretization in space and an operator-splitting technique for discretization in time. Numerical results are given for the flow inside a single-screw extruder or twin-screw extruder, which show that the fictitious domain method is efficient for the problem.