Locally Modified Version of Bott's Advection Scheme

Abstract

A simple and effective self-adjusting hybrid technique has been introduced to develop a new conservative and monotonic advection scheme that exhibits very low numerical diffusion of resolvable scales. The proposed scheme combines Bott's area-preserving flux-form algorithm with an area-preserving exponential interpolating scheme, the use of either at any particular location being automatically controlled by the local ratio of the nodal values involved in the approximation process. The performance of the combined scheme is illuminated in a series of one- and two-dimensional linear advection experiments. The comparative test calculations presented demonstrate that the combined scheme provides highly accurate solutions both in regions where the transported flow variable is smooth and in the vicinity of sharp gradients. Furthermore, the self-adjusting hybrid technique is highly effective in removing numerical artifacts such as dispersive ripples and simultaneously requires only an admissible additional computational effort relative to Bott's scheme. Thus, it is concluded that the combined scheme is well suited for many atmospheric modeling applications where advection plays a significant role.