281 research outputs found
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 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
An unfitted Nitsche method for incompressible fluid-structure interaction using overlapping meshes
We consider the extension of the Nitsche method to the case of fluid–structure interaction problems on unfitted meshes. We give a stability analysis for the space semi-discretized problem and show how this estimate may be used to derive optimal error estimates for smooth solutions,irrespectively of the mesh/interface intersection. We also discuss different strategies for the time discretization, using either fully implicit or explicit coupling (loosely coupled) schemes. Some numerical examples illustrate the theoretical discussion
A CutFEM method for two-phase flow problems
In this article, we present a cut finite element method for two-phase
Navier-Stokes flows. The main feature of the method is the formulation of a
unified continuous interior penalty stabilisation approach for, on the one
hand, stabilising advection and the pressure-velocity coupling and, on the
other hand, stabilising the cut region. The accuracy of the algorithm is
enhanced by the development of extended fictitious domains to guarantee a well
defined velocity from previous time steps in the current geometry. Finally, the
robustness of the moving-interface algorithm is further improved by the
introduction of a curvature smoothing technique that reduces spurious
velocities. The algorithm is shown to perform remarkably well for low capillary
number flows, and is a first step towards flexible and robust CutFEM algorithms
for the simulation of microfluidic devices
- …