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

Abstract

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.

Model order reduction for deforming domain problems in a time‐continuous space‐time setting

“…Examples are the Chimera method 21 or sliding interface approaches. [22][23][24] It is also worthwhile to mention the immersed boundary method, 25 where simulations are always performed on a cartesian background grid.…”

Modeling melt conveying and power consumption of co‐rotating twin‐screw extruder kneading blocks: Part A. Data generation

“…Therefore, the definition of the dimensionless flow volume was changed from that in Equation (38) to that in Equation (51), which is better suited to interpreting the results in terms of conveying and power consumption behaviors:…”

“…Since this requires boundary-conforming meshes for each position considered, computational costs are high. Several boundaryconforming methods were suggested, for example, by Elgeti et al [38][39][40] The second commonly used numerical approach involves penalty techniques, including immersed boundaries and mesh superposition techniques. Over the years, an extensive catalog of such simulation studies has accumulated.…”

A deforming‐mesh finite‐element approach applied to the large‐translation and free‐surface scenario of fused deposition modeling

“…u g is the velocity of the wall and 𝜏 b is the weak boundary condition penalty parameter. 26 It is important to mention that this contribution translates into the necessary force to stop the fluid but does not include any impact force. Therefore, this restriction is entirely appropriate for our study case, that is, filament deposition, where restitution and impact forces are negligible.…”

“…A mesh convergence study is performed, and the relative error for the temperature with respect to the analytical solution (26) is computed. In this study, we compute the elemental size as the length of the longest edge.…”