An economical second-order advection scheme for numerical weather prediction

✍ Scribed by P. Malguzzi; N. Tartagione

• Publisher: John Wiley and Sons
• Year: 1999
• Tongue: English
• Weight: 722 KB
• Volume: 125
• Category: Article
• ISSN: 0035-9009
• DOI: 10.1002/qj.49712555816

✦ Synopsis

Abstract

A very simple second‐order Eulerian scheme for the advection equation, based on a forward (backward) time integration on even (odd) grid points, is studied. the proposed scheme is similar, but not equivalent, to the so‐called ‘hopscotch method’, developed in the 1960s and early 1970s for the advection‐diffusion equation, and is stable up to Courant number 2.0. It is shown that, in the case of the advection equation, the proposed scheme has the same advantages yielded by the forward‐backward scheme in the case of the shallow‐water equations; in particular, it is equivalent to the application of centred time and space differencing on the Eliassen grid. the new scheme, unlike the classical leapfrog scheme, can be coupled to the forward‐backward integration of the gravity‐wave problem in primitive‐equation models.

With the aid of the proposed scheme, an explicit version of the atmospheric, Bologna Limited‐Area Model (developed in recent years at the FISBAT Institute of the National Council of Research of Italy) is devised, and a comparison with the semi‐implicit version of the same model is performed. the explicit version runs with a double time step, achieving the same accuracy with significantly less computer time and storage. It is suggested that the new time scheme is particularly suitable for numerical weather prediction on massively parallel computing machines based on SIMD (Single Instruction Multiple Data) and distributed memory architecture, which strongly penalize non‐local algorithms.