Improvements of the Discretization of the Incompressible Navier-Stokes Equationsin General Coordinates

摘要

The authors use a structured grid, hence the grid in the physical domain ismapped onto a rectangular grid in the computational domain. Formally, the authors assume that the mapping exists, however, actually they do not know the transformation. In fact only the coordinates of the grid points are known. Because all discretizations are carried out in the computational space, it is also necessary to transform the differential equations in this space. It has been shown that, in order to get an acceptable discretization, it is necessary to use mass fluxes as unknowns. The reason is, the transformation of a constant vector field from physical space to computational domain and backwards, results in a constant vector field. Another problem is that in a curvilinear region with no-slip walls, where the only driving force is the acceleration of gravity, still a non-zero flow field is computed. In this report, the authors shall investigate both problems into more detail and try to find an adequate solution.