Stochastic Galerkin method for cloud simulation. Part II: a fully random Navier-Stokes-cloud model

TL;DR

This paper develops and applies a stochastic Galerkin method to a fully random Navier-Stokes-cloud model, enabling uncertainty quantification in complex cloud dynamics involving fluid and microscopic processes.

Contribution

It extends previous work by incorporating randomness into the macroscopic fluid dynamics, providing a comprehensive approach for uncertainty propagation in cloud modeling.

Findings

The method accurately captures uncertainties in the coupled system.

Numerical experiments demonstrate the approach's efficiency.

The approach improves understanding of uncertainty effects in cloud simulations.

Abstract

This paper is a continuation of the work presented in [Chertock et al., Math. Cli. Weather Forecast. 5, 1 (2019), 65--106]. We study uncertainty propagation in warm cloud dynamics of weakly compressible fluids. The mathematical model is governed by a multiscale system of PDEs in which the macroscopic fluid dynamics is described by a weakly compressible Navier-Stokes system and the microscopic cloud dynamics is modeled by a convection-diffusion-reaction system. In order to quantify uncertainties present in the system, we derive and implement a generalized polynomial chaos stochastic Galerkin method. Unlike the first part of this work, where we restricted our consideration to the partially stochastic case in which the uncertainties were only present in the cloud physics equations, we now study a fully random Navier-Stokes-cloud model in which we include randomness in the macroscopic fluid dynamics as well. We conduct a series of numerical experiments illustrating the accuracy and efficiency of the developed approach.