Cut Discontinuous Galerkin Discretizations of the Incompressible Navier-Stokes Equations
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Discontinuous Galerkin methods are one of the methods of choice for the spatial discretization of transport phenomena like flow described by the incompressible Navier-Stokes equations. For the fitted mesh case, many advances have been made throughout the last decade. With this contribution, we aim to transfer the state-of-the-art fitted methods to the unfitted case using Cut Discontinuous Galerkin (CutDG) discretization. We show how to use matrix-free operator evaluation, high-order BDF time integration, and splitting schemes like pressure and velocity correction. These methods are applied to challenging benchmark test cases like the 3D Schäfer--Turek benchmark around a cylinder or flows around a sphere with geometries embedded implicitly by a level-set function. Further, we give an outlook on CutDG methods for flow around moving objects and two-phase flow.