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arXiv · 2502.09355

Simultaneous solution of incompressible Navier-Stokes flows on multiple surfaces

Michael Wolfgang Kaiser·Thomas-Peter Fries
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Abstract

A mechanical model and finite element method for the simultaneous solution of Stokes and incompressible Navier-Stokes flows on multiple curved surfaces over a bulk domain are proposed. The two-dimensional surfaces are defined implicitly by all level sets of a scalar function, bounded by the three-dimensional bulk domain. This bulk domain is discretized with hexahedral finite elements which do not necessarily conform with the level sets but with the boundary. The resulting numerical method is a hybrid between conforming and non-conforming finite element methods. Taylor-Hood elements or equal-order element pairs for velocity and pressure, together with stabilization techniques, are applied to fulfil the inf-sup conditions resulting from the mixed-type formulation of the governing equations. Numerical studies confirm good agreement with independently obtained solutions on selected, individual surfaces. Furthermore, higher-order convergence rates are obtained for sufficiently smooth solutions.

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Michael Wolfgang Kaiser, Thomas-Peter Fries. 2025-02-13. Simultaneous solution of incompressible Navier-Stokes flows on multiple surfaces. https://doi.org/10.1007/s00419-025-02935-z

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