Efficient Ensemble Methods for Predictive Fluid Flow Simulations Subject to Uncertainty

不确定性量化是预测科学中的一个中心主题，其中具有量化不确定性的模型预测对于理解和预测科学现象以及根据这些预测做出明智的决策至关重要。应用包括能源(核能、风能、太阳能等)产生、控制和制造、大气-海洋模拟、天气预报、地表水和地下水污染等。对于所有这些应用，模型问题受到许多不确定源的影响，包括不确定的模型参数、强迫函数、初始条件和边界条件。例如，在数值天气预报中，为了处理不确定的初始条件，需要用不同的初始条件多次运行天气模式，以生成可能的模式输出的集合，并根据这些数据进行分析和预测。这一过程被称为集合预报，它通常在全球所有主要的业务天气预报机构进行，包括美国国家环境预报中心和欧洲中期天气预报中心(ECMWF)。这些计算中面临的一个常见问题是存储和计算时间方面的过高成本。对于许多复杂的系统，特别是那些处理大空间尺度的系统，运行一次模型已经非常昂贵。即使在现代超级计算机上，在给定的有限计算时间内多次运行该模型也是非常具有挑战性的，在大多数大规模应用中是不可行的。因此，需要一种高效的集成仿真算法来显著降低计算成本。该项目旨在开发新颖、高效的集成算法及其分析基础，以快速计算流体流动预测模拟中的不确定性。高分辨率单一实现和计算集成之间不可避免的冲突是许多工程和地球物理应用中的一个中心困难，这些应用受输入数据和模型参数的不确定性的影响。发展能够在足够精细的空间分辨率下快速计算流动集合的有效方法具有很大的实际意义。本研究旨在开发新的、高效的集合算法来快速计算流动集合，并对新的算法和方法进行严格的数值分析。第一个研究问题是开发新的有效的集成算法来计算Boussinesq方程的多重实现。这包括开发分区集成算法，以便可以使用高度优化的Navier-Stokes方程代码来解决该问题。二是提出了基于人工压缩的集成算法的高阶时间离散化。第三个问题是开发新的、高效的集成算法来快速计算具有不同模型参数的流动集成。所研究的方法将允许有效地确定对应于许多参数集的多个解。

Uncertainty quantification is a central topic in predictive science, where model predictions with quantified uncertainties are critical for understanding and predicting scientific phenomena and making informed decisions based upon these predictions. The applications include energy (nuclear, wind, solar, etc.) generation, control and manufacturing, atmosphere-ocean modeling, weather prediction, surface water and ground water contamination, and so on. For all of these applications, the model problem is subject to numerous sources of uncertainty that include uncertain model parameters, forcing functions, initial conditions, and boundary conditions. For instance, in numerical weather prediction, to deal with uncertain initial conditions the weather model needs to be run multiple times with different initial conditions to generate an ensemble of possible model outputs, which will be analyzed and predictions made according to these data. This process is called ensemble forecasting, which is commonly done at all major operational weather prediction facilities worldwide, including the U.S. National Centers for Environmental Prediction and European Centre for Medium-Range Weather Forecasts (ECMWF). One common problem faced in these calculations is the excessive cost in terms of both storage and computing time. For many complex systems, especially those that deal with large spatial scales, running the model once is already very expensive. Running the model multiple times within a given limited computational time is very challenging even with modern supercomputers, and is not feasible in most large-scale applications. An efficient ensemble simulation algorithm that can reduce the computing cost significantly is thus highly desirable. This project seeks to develop novel, efficient ensemble algorithms and their analytical foundation for fast calculation of flow ensembles that is required to account for uncertainties in predictive simulations of fluid flows.The inevitable conflict of high-resolution single realizations and computing ensembles is a central difficulty in many engineering and geophysical applications that are subject to uncertainties in both input data and model parameters. The development of efficient methods that allow for fast calculation of flow ensembles at a sufficiently fine spatial resolution is of great practical interest. This research is to develop novel, efficient ensemble algorithms for fast calculation of flow ensembles and conduct rigorous numerical analysis for the new algorithms and methods. The first research problem is to develop new efficient ensemble algorithms to compute multiple realizations for the Boussinesq equations. This includes the development of partitioned ensemble algorithms so that highly optimized Navier-Stokes-equation codes can be used to solve the problem. The second is to advance higher-order time discretizations for ensemble algorithms based on artificial compression. The third problem is the development of novel, efficient ensemble algorithms for the fast calculation of flow ensembles with varying model parameters. The methods studied will allow efficient determination of the multiple solutions corresponding to many parameter sets.