2025/02/13 by Michael Wolfgang Kaiser, Kaiser, Michael Wolfgang, Thomas‐Peter Fries +1
Engineering · #Computational Engineering #Computational Fluid Dynamics and Aerodynamics #FOS: Computer and information sciences #Finance #Fluid Dynamics and Turbulent Flows #Lattice Boltzmann Simulation Studies #and Science (cs.CE)
paper · pdf · doi:10.48550/arxiv.2502.09355
openalex publication_date 2025/02/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
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.