Industrial and Applied Math

Date: November 12, 2018

Time: 4:00PM - 5:00PM

Location: BLOC 220

Speaker: Sourav Dutta, ERDC

Title: Reduced Order Modeling for Coastal and Hydraulic Applications in the Corps of Engineers

Abstract: Computational models are becoming increasingly important for achieving the U.S. Army Corps of Engineer's mission of delivering vital public and military engineering services. The multiphysics and multiscale problems we solve typically require sophisticated, model-specific numerical methods that are based on rigorous mathematical models. The Shallow Water Equations (SWE), for instance, are widely adopted to study various flow regimes from dam breaks and riverine flows to atmospheric processes. However, for multi-query, real-time and slim-computing scenarios arising in optimal design, risk assessment or ensemble forecasting problems, that can require thousands of forward simulations, a fully resolved two-dimensional shallow water model poses a significant computational challenge. Formal model reduction techniques like the Proper Orthogonal Decomposition (POD)-based methods are a popular choice to alleviate the computational burden. In this talk, we will review some of the work focused on the development of reduced order computational tools for supporting research on both existing and new models for coastal and hydraulic processes. We will present some efficient model reduction strategies for such complex nonlinear flows that use a combination of - 1) hyper-reduction (Discrete Empirical Interpolation Method or gappy POD), 2) non-intrusive multivariate radial basis function (RBF-NIROM) interpolation, and 3) POD in a Lagrangian frame that can effectively capture the lower rank structure of wave-like solutions even in the presence of large gradients and non-polynomial nonlinearities. We will present results involving practical dam-break scenarios and large-scale geophysical flows and discuss the accuracy, computational performance, and robustness of these methods.