论文标题
云模拟的随机Galerkin方法。第二部分：完全随机的Navier-Stokes-Cloud模型
Stochastic Galerkin method for cloud simulation. Part II: a fully random Navier-Stokes-cloud model
论文作者
论文摘要
本文是[Chertock等人，数学中介绍的作品的延续。 CLI。天气预报。 5，1（2019），65--106]。我们研究了弱压缩流体的温暖云动力学中的不确定性传播。数学模型受PDE的多尺度系统的控制，其中宏观流体动力学由弱压缩的Navier-Stokes系统描述，而微观云动力学由对流扩散 - 扩散反应系统建模。为了量化系统中存在的不确定性，我们得出并实施了广义的多项式随机盖尔金方法。与这项工作的第一部分不同，我们将考虑因素限制为仅在云物理方程中存在的不确定性的部分随机案例，我们现在研究一个完全随机的navier-stokes-cloud模型，在该模型中，我们在宏观流体动力学中也包括随机性。我们进行了一系列数值实验，以说明开发方法的准确性和效率。
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.
