Domain decomposition coupling of FV4 and DDFV for numerical weather prediction (Q2100364)

The authors present DDFV (Discrete Duality Finite Volume) scheme which does not need a mapping to a regular grid on a rectangular domain for a faithful discretization of diffusion operators on the high aspect ratio grids typical in numerical weather prediction. The scheme converges on domains which lead to discontinuities in the derivatives of the solution when a mapping to a regular grid is used. Since DDFV uses twice as many unknowns than a standard FV4, a coupled DDFV-FV4 scheme is also presented. This coupled scheme only uses DDFV where it is needed due to the mountain orography. The numerical tests show that the method is of second order for the both DDFV and DDFV-FV4 schemes and the coupled scheme is only faster when less than half the domain is treated by DDFV, even though it always has less unknowns than the DDFV method. The reason for this stems from the non-symmetry introduced by the coupling through interpolation between DDFV and FV4. For the entire collection see [Zbl 1485.65003].