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A higher order fictitious domain method for the Navier–Stokes equations
Author(s) -
Bause Markus,
Anselmann Mathias
Publication year - 2021
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.202000038
Subject(s) - discretization , finite element method , mathematics , polygon mesh , domain (mathematical analysis) , discontinuous galerkin method , navier–stokes equations , galerkin method , mathematical analysis , fictitious domain method , compressibility , stokes flow , incompressible flow , space (punctuation) , order (exchange) , flow (mathematics) , physics , geometry , mechanics , computer science , finance , economics , thermodynamics , operating system
We present a higher order approach for the numerical approximation of the Navier–Stokes equations of incompressible viscous flow on time‐dependent domains. A fictitious domain method using non body‐fitted finite element meshes for immersed and moving boundaries along with cut cell techniques is applied. Higher order discontinuous Galerkin time discretization schemes and inf‐sup stable pairs of finite elements for the discretization in space are further ingredients of the approach.