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BY 4.0 license Open Access Published by De Gruyter Open Access November 20, 2019

Stochastic Galerkin method for cloud simulation

A. Chertock , A. Kurganov , M. Lukáčová-Medvid’ová EMAIL logo , P. Spichtinger and B. Wiebe

Abstract

We develop a stochastic Galerkin method for a coupled Navier-Stokes-cloud system that models dynamics of warm clouds. Our goal is to explicitly describe the evolution of uncertainties that arise due to unknown input data, such as model parameters and initial or boundary conditions. The developed stochastic Galerkin method combines the space-time approximation obtained by a suitable finite volume method with a spectral-type approximation based on the generalized polynomial chaos expansion in the stochastic space. The resulting numerical scheme yields a second-order accurate approximation in both space and time and exponential convergence in the stochastic space. Our numerical results demonstrate the reliability and robustness of the stochastic Galerkin method. We also use the proposed method to study the behavior of clouds in certain perturbed scenarios, for examples, the ones leading to changes in macroscopic cloud pattern as a shift from hexagonal to rectangular structures.

MSC 2010: 65L05; 65M06; 35L45; 35L65; 65M25; 65M15

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Received: 2018-11-29
Accepted: 2019-11-01
Published Online: 2019-11-20

© 2019 A. Chertock et al., published by De Gruyter

This work is licensed under the Creative Commons Attribution 4.0 Public License.

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