RUI: Analysis and Numerical Solutions for Stochastic Stokes Equations

RUI：随机斯托克斯方程的分析和数值解

• 批准号: 0609918
• 负责人: Roselyn Williams
• 金额: --
• 依托单位: Florida Agricultural and Mechanical University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2006
• 资助国家: 美国
• 起止时间: 2006-08-01 至 2010-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0609918&HistoricalAwards=false
• 关键词: RUI; Analysis; Numerical; Solutions; Stochastic

The PI and colleagues study the numerical simulation of an incompressible The PI and colleagues study the numerical simulation of an incompressible viscous fluid, obeying the Stokes equations. The research will study the effect of an additional stochastic forcing term, random viscosity and random boundary values . Methods of constructing families of solutions will be used and compared. The PI is interested in the relationship between uncertainty in the input (forcing term) to the uncertainty in the output (solution values used to estimate expected values.) The research has three major components: 1. Monte Carlo methods enhanced with sensitivity derivatives, for the stochastic Stokes equations with random input parameters; 2. finite element approximation of stochastic Stokes equations with white noise forcing terms; 3. the stochastic spectral finite element method with polynomial chaos spaces, with random coefficients and boundary conditions. Computer calculations can seem deceptively precise. But scientists have discovered that there is a significant amount of uncertainty in all physical systems; not just when something is measured, but even when an attempt is made to describe how the system changes. No computer calculation can possibly consider every slight variation in the measurements and dynamics of a system under study. And yet it is known that, at least in some cases, small amounts of uncertainty can lead to significant, and even disastrous, errors in the computed results. The proposed research is one example of the effort to understand, quantify and control the effect of uncertainties, in this case, for a standard physical computation involving the flow of a fluid. An important bonus of this research is the involvement of a group of largely minority students, who will receive the support, guidance and training necessary to begin scientific careers.

PI及其同事研究不可压缩粘性流体的数值模拟，遵守斯托克斯方程。研究将研究附加随机强迫项、随机粘性和随机边界值的影响。构建家庭的解决方案的方法将被使用和比较。 PI感兴趣的是输入（强迫项）的不确定性与输出（用于估计预期值的解值）的不确定性之间的关系。该研究有三个主要组成部分： 1.蒙特卡罗方法增强了灵敏度导数， 对于具有随机输入参数的随机Stokes方程; 2.随机有限元逼近 具有白色噪声强迫项的斯托克斯方程 3.随机谱有限元法 多项式混沌空间，随机系数， 边界条件 计算机计算可能看起来精确得令人难以置信。 但科学家们发现，所有的物理系统都存在大量的不确定性，不仅是在测量时，甚至在试图描述系统如何变化时也是如此。任何计算机计算都不可能考虑所研究系统的测量和动力学的每一个微小变化。 然而，众所周知，至少在某些情况下，少量的不确定性可能导致计算结果中的重大甚至灾难性的错误。 拟议的研究是努力理解，量化和控制不确定性的影响的一个例子，在这种情况下，对于涉及流体流动的标准物理计算。这项研究的一个重要好处是一组主要是少数民族学生的参与，他们将获得开始科学生涯所需的支持、指导和培训。