Uncertainty Quantification for Hyperbolic Conservation Laws with Flux Coefficients Given by Spatiotemporal Random Fields
Uncertainty Quantification for Hyperbolic Conservation Laws with Flux Coefficients Given by Spatiotemporal Random Fields
复制标题
时空随机场通量系数双曲守恒定律的不确定性量化
DOI：
10.1137/15m1027723
复制
发表时间：
2015
期刊：
影响因子：
--
通讯作者：
F. Fuchs
中科院分区：
文献类型：
--
作者：
A. Barth;F. Fuchs
本文讨论了具有随机系数的双曲型偏微分方程解。我们考虑了具有时空随机场模型系数的通量函数的挑战性问题。这些场由空间上的相关高斯随机场和时间上的Ornstein-Uhlenbeck过程给出。由此得到的方程系统由每个随机参数的随机微分方程组成，耦合到双曲守恒定律。我们定义了一个适当的解的概念，并分析了离散化方法的误差和收敛。提出了一种新的基于蒙特卡罗有限体积法的离散框架，用于稳健计算随机双曲偏微分方程解的矩。我们给出了两个应用中的例子：磁感应方程和线性声学，两者都具有时空随机背景速度场。
In this paper hyperbolic partial differential equations with random coefficients are discussed. We consider the challenging problem of flux functions with coefficients modeled by spatiotemporal random fields. Those fields are given by correlated Gaussian random fields in space and Ornstein-Uhlenbeck processes in time. The resulting system of equations consists of a stochastic differential equation for each random parameter coupled to the hyperbolic conservation law. We define an appropriate solution concept in his setting and analyze errors and convergence of discretization methods. A novel discretization framework, based on Monte Carlo Finite Volume methods, is presented for the robust computation of moments of solutions to those random hyperbolic partial differential equations. We showcase the approach on two examples which appear in applications: The magnetic induction equation and linear acoustics, both with a spatiotemporal random background velocity field.
影响因子：
0.9
作者：
Lang, Annika;Potthoff, Juergen
通讯作者：
Potthoff, Juergen