8.7 Coordinate Cut 坐标切割[cfd-8-7]

This type of boundary condition is encountered only in the case of structured grids. The coordinate cut represents an artificial, not a physical, boundary. It is a line (plane in 3D) composed of grid points with different computational coordinate(s) but the same physical location. This means that the grid is folded such that it touches itself. As we shall see in Subsection 11.1.1, the coordinate cut appears for the so-called C- (Fig. 11.5) or O-grid topology (Fig. 11.9). The flow variables and their gradients have to stay continuous across the cut.

The best way to implement the cut boundary condition is to employ dummy cells (points). The situation is sketched in Fig. 8.9. As we can see, the dummy layers here are not virtual, but they coincide with the grid on the opposite side of the cut. Hence, the values of physical quantities in the dummy cells (cell-centred scheme), or in the dummy points (cell-vertex scheme), are obtained directly from the opposite cells (points). In the case of the cell-centred scheme, the fluxes across the faces of the boundary cell (shaded in Fig. 8.9a) are evaluated exactly like in the interior field.

The cut boundary can be treated in two different ways for the cell-vertex scheme. One possibility is to generate a complete control volume at the cut (the second part is denoted by a dashed line in Fig. 8.9b). Using the dummy points, the fluxes can be calculated in the same way as inside the domain. If the implementation is done correctly, the flow quantities at the points 2 (upper grid part) and 5 (lower part) will be equal. The second approach is to integrate the fluxes separately for each half of the control volume. The residuals at the points 2 and 5 in Fig. 8.9b are then added. It is important that the partial control volumes at the points 2 and 5 are summed up as well.