Extended finite element method for viscous flow inside complex three-dimensional geometries with moving internal boundaries

A three-dimensional extended finite element method is presented to simulate Stokes flow in complex geometries with internal moving parts. Instead of re-meshing the flow domain, the kinematics of the internal objects are imposed on the conservation equations using a constraint, implemented with a Lagrangian multiplier. To capture discontinuities of field variables, such as pressure and velocity, on the intersected elements, XFEM is used. To validate our method, it is first applied to a relatively simple problem, that is, the flow around a cylinder in a channel. The results are verified by comparing with a boundary-fitted solution. After validation of the model and its implementation, the three-dimensional flow in a twin-screw extruder is simulated and the results are compared with experimental data from literature. XFEM shows very good accuracy for complex geometries with internal moving parts and narrow gap regions where the shear rate is orders of magnitude higher than in other regions.