A Multimoment Constrained Finite-Volume Model for Nonhydrostatic Atmospheric Dynamics

Xingliang Li State Key Laboratory of Severe Weather, Chinese Academy of Meteorological Sciences, and Center of Numerical Weather Prediction, China Meteorological Administration, Beijing, China

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Chungang Chen School of Human Settlement and Civil Engineering, Xi’an Jiaotong University, Xi’an, Shaanxi, China

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Xueshun Shen State Key Laboratory of Severe Weather, Chinese Academy of Meteorological Sciences, and Center of Numerical Weather Prediction, China Meteorological Administration, Beijing, China

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Feng Xiao Department of Energy Sciences, Tokyo Institute of Technology, Yokohama, Japan

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Abstract

The two-dimensional nonhydrostatic compressible dynamical core for the atmosphere has been developed by using a new nodal-type high-order conservative method, the so-called multimoment constrained finite-volume (MCV) method. Different from the conventional finite-volume method, the predicted variables (unknowns) in an MCV scheme are the values at the solution points distributed within each mesh cell. The time evolution equations to update the unknown point values are derived from a set of constraint conditions based on the multimoment concept, where the constraint on the volume-integrated average (VIA) for each mesh cell is cast into a flux form and thus guarantees rigorously the numerical conservation. Two important features make the MCV method particularly attractive as an accurate and practical numerical framework for atmospheric and oceanic modeling. 1) The predicted variables are the nodal values at the solution points that can be flexibly located within a mesh cell (equidistant solution points are used in the present model). It is computationally efficient and provides great convenience in dealing with complex geometry and source terms. 2) High-order and physically consistent formulations can be built by choosing proper constraints in view of not only numerical accuracy and efficiency but also underlying physics. In this paper the authors present a dynamical core that uses the third- and the fourth-order MCV schemes. They have verified the numerical outputs of both schemes by widely used standard benchmark tests and obtained competitive results. The present numerical core provides a promising and practical framework for further development of nonhydrostatic compressible atmospheric models.

Corresponding author address: Xingliang Li, Center of Numerical Weather Prediction, China Meteorological Administration, 46 Zhongguancun South St., Beijing 100081, China. E-mail: lixl@cams.cma.gov.cn

Abstract

The two-dimensional nonhydrostatic compressible dynamical core for the atmosphere has been developed by using a new nodal-type high-order conservative method, the so-called multimoment constrained finite-volume (MCV) method. Different from the conventional finite-volume method, the predicted variables (unknowns) in an MCV scheme are the values at the solution points distributed within each mesh cell. The time evolution equations to update the unknown point values are derived from a set of constraint conditions based on the multimoment concept, where the constraint on the volume-integrated average (VIA) for each mesh cell is cast into a flux form and thus guarantees rigorously the numerical conservation. Two important features make the MCV method particularly attractive as an accurate and practical numerical framework for atmospheric and oceanic modeling. 1) The predicted variables are the nodal values at the solution points that can be flexibly located within a mesh cell (equidistant solution points are used in the present model). It is computationally efficient and provides great convenience in dealing with complex geometry and source terms. 2) High-order and physically consistent formulations can be built by choosing proper constraints in view of not only numerical accuracy and efficiency but also underlying physics. In this paper the authors present a dynamical core that uses the third- and the fourth-order MCV schemes. They have verified the numerical outputs of both schemes by widely used standard benchmark tests and obtained competitive results. The present numerical core provides a promising and practical framework for further development of nonhydrostatic compressible atmospheric models.

Corresponding author address: Xingliang Li, Center of Numerical Weather Prediction, China Meteorological Administration, 46 Zhongguancun South St., Beijing 100081, China. E-mail: lixl@cams.cma.gov.cn
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