Numerical method for calculation of the incompressible flow in general curvilinear co-ordinates with double staggered grid

A solution methodology has been developed for incompressible flow in general curvilinear co-ordinates. Two staggered grids are used to discretize the physical domain. The first grid is a MAC quadrilateral mesh with pressure arranged at the centre and the Cartesian velocity components located at the middle of the sides of the mesh. The second grid is so displaced that its corners correspond to the centre of the first grid. In the second grid the pressure is placed at the corner of the first grid. The discretized mass and momentum conservation equations are derived on a control volume. The two pressure grid functions are coupled explicitly through the boundary conditions and implicitly through the velocity of the field. The introduction of these two grid functions avoids an averaging of pressure and velocity components when calculating terms that are generated in general curvilinear co-ordinates. The SIMPLE calculation procedure is extended to the present curvilinear co-ordinates with double grids. Application of the methodology is illustrated by calculation of well-known external and internal problems: viscous flow over a circular cylinder, with Reynolds numbers ranging from 10 to 40, and lid-driven flow in a cavity with inclined walls are examined. The numerical results are in close agreement with experimental results and other numerical data.