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.
