  In this work a Nitsche-based imposition of generalized Navier conditions on
cut meshes for the Oseen problem is presented. Other methods from literature
dealing with the generalized Navier condition impose this condition by means of
substituting the tangential Robin condition in a classical Galerkin way. These
methods work fine for a large slip length coefficient but lead to conditioning
and stability issues when it approaches zero. We introduce a novel method for
the weak imposition of the generalized Navier condition which remains
well-posed and stable for arbitrary choice of slip length, including zero. The
method proposed here builds on the formulation done by [1]. They impose a Robin
condition for the Poisson problem by means of Nitsche's method for an arbitrary
combination of the Dirichlet and Neumann parts of the condition. The analysis
conducted for the proposed method is done in a similar fashion as in [2], but
is done here for a more general type of boundary condition. The analysis proves
stability for all flow regimes and all choices of slip lengths. Also an
L2-optimal estimate for the velocity error is shown, which was not conducted in
the previously mentioned work. A numerical example is carried out for varying
slip lengths to verify the robustness and stability of the method with respect
to the choice of slip length. Even though proofs and formulations are presented
for the more general case of an unfitted grid method, they can easily be
reduced to the simpler case of a boundary-fitted grid with the removal of the
ghost-penalty stabilization terms.
