THIS IS A CONTINUATION OF N00014-14-1-0520 A Physics-Constrained Order-Reduction Framework for the Dynamical Description of Subspaces-of-Interest in Turbulent Dynamical Systems
Abstract
Objective: Novel computational methods will be developed for two specific application fields: i) A reduced-order model for the uncertainty quantification of quantities-of-interest for a multi-physics problem involving a non-homogeneous turbulent flow with thermal interactions: a cool jet in a crossflow of a hot gas; and ii) The formulation of reduced-order models for nonlinear water waves that will allow for the statistical quantification and the prediction of extreme events. A successful implementation of the proposed order-reduction method will have significant practical impact on fields such as optimization, control, and filtering of fluid flows as well as on the development of practical prediction methods for twodimensional nonlinear wave fields in the ocean. In particular, this project consists of the following specific objectives: a) Implementation of a basis extraction algorithm that will compute the relevant basis for strongly transient and turbulent flows using existing numerical codes and without the need for implementation of expensive stochastic solvers. b) Formulation of suitable inner products that will result in (using the previous algorithm) the adaptive computation of subspaces that are relevant to the desired information, e.g. large-scale structure of the flow, or structure of intermittent extreme events etc. c) Development and implementation of a new order-reduction approach for high-dimensional systems that will combine reduced-order information from dynamical equations with energy fluxes obtained through available spectral information. d) Development of multi-level information-theoretic measures that will account for different form of statistical information for different modes. This will be used for the assessment and improvement of the order-reduction scheme proposed. e) Application of the blended order-reduction scheme to the uncertainty quantification of large scale quantities of interest for a multi-physics problem involving a nonhomogeneous turbulent flow with thermal interactions: a cool jet in a crossflow of a hot gas. f) Application of the developed order-reduction scheme for the efficient description of the modes associated with extreme events in nonlinear waves and the subsequent formulation of conditions for their occurrence under a given water waves spectrum. Approach: The PI will develop the theoretical core for a novel stochastic order-reduction technique for turbulent flows and nonlinear wave systems exhibiting extreme event behavior. The new technique will combine the dynamical system equations as well as available spectral information. Also, the PI will apply the new technique on a specific turbulent flow a cool jet in a cross-flow of a hot gas. Through the implementation of a reduced-order methodology on this flow the contractor will assess the capacity of the new scheme to predict the properties-of-interest for the flow when various parameters are modified. Finally, the PI will apply the new technique on the development of reducer-order models for the description of rare or extreme events in nonlinear wave equations (modeling water waves). The reduced-order models will be able to measure accurately the probability of occurrence of an extreme event using the spectrum of the nonlinear system - information that is usually available for these problems through measurements.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Jun 03, 2016
- Source ID
- N000141612124
Entities
People
- Themistoklis Sapsis
Organizations
- Massachusetts Institute of Technology
- Office of Naval Research
- United States Navy