Treatment of Slip Boundary Conditions for the Incompressible Navier-StokesEquations in General Co-ordinates

摘要

In van Kan et al. (1990), the numerical discretization of the incompressibleNavier-Stokes equations in general curvilinear co-ordinates is treated. The discretization is based upon a regular, curvilinear, boundary fitted grid. For the discretization, a finite volume method is used. The curvilinear grid is mapped onto a rectangular computational grid by a geometrical transformation, which is implicitly defined by the co-ordinates of the grid points. Van Kan et al. treat, apart from the discretization in the inner region, boundary conditions of the following types: (1) Dirichlet boundary conditions, i.e. velocity prescribed; (2) Natural boundary conditions, i.e. normal and tangential stress given; (3) Semi-natural outflow condition, i.e. normal stress and tangential velocity given. It is the authors aim to extend the existing model with turbulence equations. As slip boundary conditions are not treated in van Kan et al., the report is devoted to the discretization of the Navier-Stokes equations with slip boundary conditions.