Conservative Transport Using a Compact Third-Order Scheme on the Yin–Yang Grid

The Yin–Yang grid, while offering advantages such as quasi-uniformity and pole-singularity avoidance, inherently lacks global conservation due to interpolation at grid boundaries. To address this problem, we proposed a compact flux correcting method to ensure conservation based on a third-order Multi-moment Constrained Finite-Volume scheme (MCV3). With the nine point values within each computational cell, a bivariate quadratic polynomial was constructed for high-fidelity boundary interpolation and flux reconstruction. Identical flux across the boundary of the overlapped grid was enforced in the Yin and Yang components with the help of the polynomial. A third-order conservative advection scheme was therefore achieved on the Yin–Yang grid, which effectively balance the numerical accuracy and computational efficiency. Several standard numerical tests were carried out to confirm the performance of the interpolation algorithm and the conservation calculation scheme. The results reveal that the high accuracy and stability of the strict conservation scheme are helpful in passive transport situations on Yin–Yang grids.