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An Accurate Semi-Lagrangian Scheme for Raindrop Sedimentation

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  • 1 Department of Energy Sciences, Tokyo Institute of Technology, and Frontier Research System for Global Change, Integrated Modeling Research Program, Yokohama, Japan
  • | 2 Department of Energy Sciences, Tokyo Institute of Technology, Yokohama, Japan
  • | 3 Saitama Institute of Technology, Saitama, and Frontier Research System for Global Change, Integrated Modeling Research Program, Yokohama, Japan
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Abstract

An accurate method for explicitly computing the transport of rainwater is devised and tested. The scheme is conservative and positive definite. A cubic polynomial is employed to approximate the spatial distribution of the rainwater; thus, the resulting scheme is of high accuracy. With a slope modification, numerical oscillations can be easily eliminated in the vicinity of large gradients. Being essentially of Lagrangian type, the scheme is stable even with a Courant–Friedrichs–Lewy number larger than 1. The scheme was tested with the numerical example of Kato and was found to have a computational stability similar to the box-Lagrangian scheme, but it is more accurate.

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

An accurate method for explicitly computing the transport of rainwater is devised and tested. The scheme is conservative and positive definite. A cubic polynomial is employed to approximate the spatial distribution of the rainwater; thus, the resulting scheme is of high accuracy. With a slope modification, numerical oscillations can be easily eliminated in the vicinity of large gradients. Being essentially of Lagrangian type, the scheme is stable even with a Courant–Friedrichs–Lewy number larger than 1. The scheme was tested with the numerical example of Kato and was found to have a computational stability similar to the box-Lagrangian scheme, but it is more accurate.

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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