  For most finite element simulations, boundary-conforming meshes have
significant advantages in terms of accuracy or efficiency. This is particularly
true for complex domains. However, with increased complexity of the domain,
generating a boundary-conforming mesh becomes more difficult and time
consuming. One might therefore decide to resort to an approach where individual
boundary-conforming meshes are pieced together in a modular fashion to form a
larger domain. This paper presents a stabilized finite element formulation for
fluid and temperature equations on sliding meshes. It couples the solution
fields of multiple subdomains whose boundaries slide along each other on common
interfaces. Thus, the method allows to use highly tuned boundary-conforming
meshes for each subdomain that are only coupled at the overlapping boundary
interfaces. In contrast to standard overlapping or fictitious domain methods
the coupling is broken down to few interfaces with reduced geometric dimension.
The formulation consists of the following key ingredients: the coupling of the
solution fields on the overlapping surfaces is imposed weakly using a
stabilized version of Nitsche's method. It ensures mass and energy conservation
at the common interfaces. Additionally, we allow to impose weak Dirichlet
boundary conditions at the non-overlapping parts of the interfaces. We present
a detailed numerical study for the resulting stabilized formulation. It shows
optimal convergence behavior for both Newtonian and generalized Newtonian
material models. Simulations of flow of plastic melt inside single-screw as
well as twin-screw extruders demonstrate the applicability of the method to
complex and relevant industrial applications.
