A high‐order vertical discretization method for a semi‐implicit mass‐based non‐hydrostatic kernel. (28th July 2015)

• Record Type: Journal Article
• Authors: Yang, Jinhui; Song, Junqiang; Wu, Jianping; Ren, KaiJun; Leng, Hongze
• Is Part Of: Quarterly journal of the Royal Meteorological Society. Volume 141:Number 692(2015:Oct.)
• Page Start: 2880
• Page End: 2885
• Publication Date: 2015-07-28
• Subjects: mass‐based coordinate -- non‐hydrostatic kernel -- finite‐element vertical discretization; Meteorology -- Periodicals; 551.5
• DOI: 10.1002/qj.2573
• Languages: English
• ISSNs: 0035-9009

Abstract

Abstract : Applying finite‐element vertical discretization to a mass‐based non‐hydrostatic kernel has proved difficult due to the constraints of vertical operators. This article proposes a novel hybrid finite‐element vertical discretization method for a semi‐implicit mass‐based non‐hydrostatic kernel, which integrates a finite‐differential scheme and a finite‐element scheme. In the hybrid method, the finite‐differential scheme which satisfies the set of constraints is applied to the linear part, while a cubic finite‐element scheme with high‐order accuracy is applied to the non‐linear part. Furthermore, to improve the accuracy of the linear part, an enlarged set of vertical levels is applied to the differential scheme. This set of vertical levels is only used to solve semi‐implicit equations, and has no impact on the grid point calculation and spectral transformations. A series of 2D idealized test cases are conducted to verify the stability and the accuracy of our new method.