Adaptively implicit MPDATA advection for arbitrary Courant numbers and meshes

Advection schemes with time step restrictions are widely used in weather and climate models. This can lead to instability the presence of high flow speeds (relative mesh spacing) such as occurs convective updraughts, regions convergence, or where winds unusually high. An adaptively implicit advection scheme is proposed that treats implicitly only Courant number Flux correction ensure monotonicity adapted work stepping. A version multidimensional positive-definite transport algorithm MPDATA derived an anti-diffusive flux compensating truncation errors off-centred The gradually reduced numbers increase above 2 order maintain stability at expense second-order accuracy numbers. Results two-dimensional by deformational presented on various meshes sphere. Stability maintained when over 100 a small region, strong wind crosses poles rotated latitude–longitude mesh. Good solutions also obtained skipped mesh, cubed sphere, hexagonal meshes. Accuracy reverts first large fraction domain.