Non-Conforming Interfaces¶
Non-conforming interfaces allow the usage of non-matching, interacting grids connected by an interface. In the following explanation the Nitsche method 1 is presented, because it more robust in practical applications 2. For a detailed deriviation look into 1 and 2.
Consequently, non-conforming interfaces allow to use different meshes in the same simulation, as shown in the above figure. Both domains, \Omega_1 and \Omega_2 exist of different grids and are connected by the non-conform interface \Gamma_I. This is especially interesting if different materials are taken into account while a coupled simulation is performed. Furthermore, they are used for simulate rotating structures (for more details look into Features -> Rotating Interfaces) 3.
For defining a non-conform interface first the surfaces, that are part of the interface, can be defined (just to have a better overview, not necessarily needed for the functionality). Additionally, the non conforming interface must be defined within the domain element. (Arbitrary names are marked as *)
<domain geometryType="*">
<regionList>
<region name="*" material="*"/>
</regionList>
<surfRegionList>
<surfRegion name="*" />
<surfRegion name="*" />
</surfRegionList>
<ncInterfaceList>
<ncInterface name="*" primarySide="*" secondarySide="*"/>
<ncInterfaceList>
</domain>
The nc-interface must then be declared once again in the respective PDE where it should occur, e.g.,
<pdeList>
<acoustic formulation="acouPressure">
<regionList>
<region name="*"/>
</regionList>
<ncInterfaceList>
<ncInterface name="*" nitscheFactor="100" formulation="Nitsche"/>
</ncInterfaceList>
</acoustic>
...
</pdeList>
An alternative coupling method is the classic Mortar FEM, which employs a Lagrange multiplyer to establish the coupling. A Mortar interface can be declared similar to the Nitsche-type Mortar, e.g.,
<pdeList>
<acoustic formulation="acouPressure">
<regionList>
<region name="*"/>
</regionList>
<ncInterfaceList>
<ncInterface name="*" formulation="Mortar"/>
</ncInterfaceList>
</acoustic>
</pdeList>
It is also possible to establish an nc-interface between the realms of different PDEs, which can be done in the coupling list, e.g., for acoustic-mechanic coupling,
<couplingList>
<direct>
<acouMechDirect>
<ncInterfaceList>
<ncInterface name="*"/>
</ncInterfaceList>
</acouMechDirect>
</direct>
</couplingList>
There are several other tags available to the non-conforming interfaces. Please refer to the XSD scheme documentation for further information.
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M. Kaltenbacher. Numerical Simulation of Mechatronic Sensors and Actuators: Finite Elements for Computational Multiphysics. Springer Berlin Heidelberg, 2015. ISBN 978-3-642-40169-5. URL: https://www.springer.com/de/book/9783642401695. ↩↩
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Andreas Hüppe, Jens Grabinger, Manfred Kaltenbacher, Aaron Reppenhagen, Gerhard Dutzler, and Wolfram Kühnel. A non-conforming finite element method for computational aeroacoustics in rotating systems. In 20th AIAA/CEAS Aeroacoustics Conference, 2739. 2014. ↩↩↩
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Stefan Schoder, Clemens Junger, and Manfred Kaltenbacher. Computational aeroacoustics of the eaa benchmark case of an axial fan. Acta Acustica, 4(5):22, 2020. ↩