Final answer:
Corner transport schemes consider both primary and diagonal directions for advection, providing improved accuracy in certain scenarios.
Step-by-step explanation:
The main difference between corner transport and regular advection schemes lies in how they handle the approximation of advection. In the regular advection scheme, models use 1D flux approximations for the derivatives in the x, y, and z directions. These flux approximations are then plugged into the advection equation to account for the transport of a quantity in the x-direction.
On the other hand, corner transport schemes take a different approach. They account for the transport of a quantity not only in the primary x-direction, but also in the diagonal directions (e.g., the corners of cells). This is done by using 2D flux approximations that incorporate the diagonal derivatives as well as the primary derivatives.
By considering the diagonal directions, corner transport schemes can provide more accurate solutions in regions where advection is important.
Overall, corner transport schemes offer a more comprehensive approach to advection by considering the diagonal directions alongside the primary directions, leading to improved accuracy in certain scenarios.