One of the types of overset grids used to cover the entire surface of the sphere is called the Yin–Yang grid. Since, in this grid, each of Yin and Yang grid components form part of the sphere, the computed fields on each of the two grids must be used to set the boundary conditions for the other grid. To this end, two methods of interpolation are used: bilinear and bicubic. Further, the periodic and open boundary conditions are applied and their results are compared. It turns out that applying the open boundary condition to numerical solution of the advection equation on the Yin-Ying grid increases the global error and results in wave damping, while the use of the periodic boundary condition leads to much higher accuracy. Another conclusion is that the use of the bicubic interpolation reduces error compared to the bilinear interpolation.