新型有限体积元方法及其在随机地球流体力学中的应用研究

项目名称： 新型有限体积元方法及其在随机地球流体力学中的应用研究

项目编号： No.11471166

项目类型： 面上项目

立项/批准年度： 2015

项目学科： 数理科学和化学

项目作者： 张志跃

作者单位： 南京师范大学

项目金额： 72万元

中文摘要： 数值天气预报是计算地球流体力学中的核心问题之一，数值预报结果的不确定性在很大程度上造成了气象预报不准确。研究预报结果不确定性产生的原因和机制，寻找减小不确定性的方法和途径是非常有意义的课题。大气运动模式可以描述为非线性随机偏微分方程组。本项目重点以随机准地转(QG)方程组为研究对象，发展可揭示大气非线性本质、适合随机大气模式的、稳定且能长时间准确积分的数值算法的新逼近理论和数值分析；设计和构造在保物理性质的同时，可以对概率空间高维性产生的大量数值计算进行高效处理的新型能量守恒有限体积元方法，从而探求新方法在实际预报业务中的应用，寻找减小数值预报不确定性的数学方法，为我国设计高效、精确、稳定的数值预报模式，提高预报准确率提供新的思路。

中文关键词： 随机地球流体力学；有限体积元方法；数值天气预报；不确定性

英文摘要： Numerical weather forecast is one of core problems in computational geostrophic fluid dynamics. The uncertainty of numerical predition has greatly caused inaccurate weather prediction. It is a significant subject to study the factors and mechanisms that yield the uncertainty of numerical predition and develop new methods to reduce the uncertainty. The modeling of atmospheric motion can be described as nonlinear stochastic partial differential equations. This proposal will focus on stochastic qusigeostrophic equations to develop new numerical algorithms that can reveal atmospheric nonlinear and stochastic natures and provide long term accurate predictions; to develop approximate theory and numerical analysis of the new numerical algorithm. The proposed new methods will be based on stable and energy conservative finite volume element methods that not only keep phyical properties, but also efficiently process substantial numerical computational loads which comes from higher dimensional problem of probability space. Then we can seek the applications of new method in practical prediction, search mathematical methods which reduce uncertainties of numerical prediction,to provide new ideas for designing effective, accurate and stable numerical prediction modeling, and improving accuracy rate of numerical prediction in our country.

英文关键词： Stochastic Geostrophic Fliud Dynamics;Finite Volume Element Methods;Numerical Weather Forecast;Uncertainty