NUMERICALLY MODELING STOCHASTIC LIE TRANSPORT IN FLUID DYNAMICS
NUMERICALLY MODELING STOCHASTIC LIE TRANSPORT IN FLUID DYNAMICS
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DOI：
10.1137/18m1167929
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发表时间：
2019-01-01
影响因子：
1.6
通讯作者：
Shevchenko, Igor
中科院分区：
文献类型：
--
作者：
Cotter, Colin J.;Crisan, Dan;Shevchenko, Igor
本文对理想流体中的随机输运问题进行了数值研究。根据霍尔姆[Proc. A，471（2015）]和Cotter，Gottwald和霍尔姆[Proc. A，473（2017）]，变换理论和多时间均匀化的原理分别意味着一种物理上有意义的数据驱动方法，用于将流体传输速度分解为某类流体流动的漂移和随机部分。在本文中，我们开发了一种新的方法来实现这种速度分解，然后用有限元离散化不可压缩二维（2D）欧拉流体流动的数值积分所产生的随机偏微分方程。在这种情况下，这里测试的新方法被认为是适合粗粒化。具体而言，我们进行不确定性量化测试的速度分解的科特，Gottwald和霍尔姆，通过比较合奏的粗网格实现的解决方案所产生的随机偏微分方程的“真解”的确定性流体偏微分方程，计算在一个精细的网格。时间离散用于逼近随机偏微分方程的解决方案是一致的。我们包括全面的数值试验，确认不可压缩的二维欧拉流体流动的情况下的流函数，速度和涡度场的非高斯性。
We present a numerical investigation of stochastic transport in ideal fluids. According to Holm [Proc. A, 471 (2015)] and Cotter, Gottwald, and Holm [Proc. A, 473 (2017)], the principles of transformation theory and multitime homogenization, respectively, imply a physically meaningful, data-driven approach for decomposing the fluid transport velocity into its drift and stochastic parts for a certain class of fluid flows. In the current paper, we develop a new methodology to implement this velocity decomposition and then numerically integrate the resulting stochastic partial differential equation using a finite element discretization for incompressible two-dimensional (2D) Euler fluid flows. The new methodology tested here is found to be suitable for coarse-graining in this case. Specifically, we perform uncertainty quantification tests of the velocity decomposition of Cotter, Gottwald, and Holm, by comparing ensembles of coarse grid realizations of solutions of the resulting stochastic partial differential equation with the "true solutions" of the deterministic fluid partial differential equation, computed on a refined grid. The time discretization used for approximating the solution of the stochastic partial differential equation is shown to be consistent. We include comprehensive numerical tests that con firm the non-Gaussianity of the streamfunction, velocity, and vorticity fields in the case of incompressible 2D Euler fluid flows.