Combining boundary-conforming finite element meshes on moving domains using a sliding mesh approach

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 article 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 nonoverlapping parts of the interfaces. We present a detailed numerical study for the resulting stabilized formulation. It shows optimal convergence behavior of the interface coupling 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.

Automated summary

Boundary-conforming meshes offer advantages in accuracy and efficiency for finite element simulations, but become more challenging to generate with increased domain complexity. Piecing together individual boundary-conforming meshes in a modular fashion allows for coupling of solution fields at overlapping boundary interfaces, utilizing highly tuned meshes for each subdomain. The method ensures mass and energy conservation at common interfaces, with optimal convergence behavior demonstrated for Newtonian and generalized Newtonian material models in complex industrial applications such as plastic extruders.