A Finite-Volume Grid Using Multimoments for Geostrophic Adjustment

F. Xiao Department of Energy Sciences, Tokyo Institute of Technology, Yokohama, Japan, and State Key Laboratory of Severe Weather, Chinese Academy of Meteorological Sciences, Beijing, China

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X. D. Peng Earth Simulator Center, Yokohama, Japan

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X. S. Shen State Key Laboratory of Severe Weather, Chinese Academy of Meteorological Sciences, Beijing, China

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Abstract

This paper presents a novel finite-volume grid that uses not only the volume-integrated average (VIA) like the traditional finite-volume method, but also the surface-integrated average (SIA) as the model variables. The VIA and SIA are generically called “moments” in the context used here and are carried forward in time separately as the prognostic quantities. With the VIA defined in the control volume while the SIA is on the surface of the control volume, the discretization based on VIA and SIA leads to some new features in the numerical dispersions. A simple formulation using both VIA and SIA for shallow-water equations is presented. The numerical dispersion of the resulting grid, which is denoted as the “M grid,” is discussed with comparisons to the existing ones.

Corresponding author address: Feng Xiao, Department of Energy Sciences, Tokyo Institute of Technology, 4259 Nagatsuta, Midori-ku, Yokohama 226-8502, Japan. Email: xiao@es.titech.ac.jp

Abstract

This paper presents a novel finite-volume grid that uses not only the volume-integrated average (VIA) like the traditional finite-volume method, but also the surface-integrated average (SIA) as the model variables. The VIA and SIA are generically called “moments” in the context used here and are carried forward in time separately as the prognostic quantities. With the VIA defined in the control volume while the SIA is on the surface of the control volume, the discretization based on VIA and SIA leads to some new features in the numerical dispersions. A simple formulation using both VIA and SIA for shallow-water equations is presented. The numerical dispersion of the resulting grid, which is denoted as the “M grid,” is discussed with comparisons to the existing ones.

Corresponding author address: Feng Xiao, Department of Energy Sciences, Tokyo Institute of Technology, 4259 Nagatsuta, Midori-ku, Yokohama 226-8502, Japan. Email: xiao@es.titech.ac.jp

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