论文标题
Navier-Stokes方程的随机宣传学方法具有自适应时间步长
A stochastic Galerkin method with adaptive time-stepping for the Navier-Stokes equations
论文作者
论文摘要
我们在随机有限元离散化的背景下研究时间依赖的Navier-Stokes方程。具体而言，我们假设粘度是以广义多项式膨胀形式给出的一个随机场，并且我们使用随机的Galerkin方法将方法扩展到[D. D. A. Kay等人，\ textit {Siam J. Sci。计算} 32（1），第111--128页，2010年]。对于由此产生的随机问题，我们探讨了所得随机溶液的性质，还将结果与蒙特卡洛和随机搭配的结果进行了比较。由于时间步骤方案是完全隐式的，因此我们还提出了使用预处理的Krylov子空间方法有效解决随机盖金线性系统的策略。数值实验说明了随机盖尔金方法的有效性。
We study the time-dependent Navier-Stokes equations in the context of stochastic finite element discretizations. Specifically, we assume that the viscosity is a random field given in the form of a generalized polynomial chaos expansion, and we use the stochastic Galerkin method to extend the methodology from [D. A. Kay et al., \textit{SIAM J. Sci. Comput.} 32(1), pp. 111--128, 2010] into this framework. For the resulting stochastic problem, we explore the properties of the resulting stochastic solutions, and we also compare the results with that of Monte Carlo and stochastic collocation. Since the time-stepping scheme is fully implicit, we also propose strategies for efficient solution of the stochastic Galerkin linear systems using a preconditioned Krylov subspace method. The effectiveness of the stochastic Galerkin method is illustrated by numerical experiments.
