Parametrized Model Order Reduction for Engineered Coastal and Hydraulic Systems: Component Libraries and Digital Twins
Abstract
Statement of Objectives. We develop a port-reduced reduced-basis (RB) component approach (PR-RBC) for the partial differential equations (PDEs) which govern flow in riverine and coastal environments: the diffusive wave equation; the shallow-water (Saint Venant) equations; (small-amplitude) free-surface Navier-Stokes. The methods can be applied in two contexts: the analysis of a new hydraulic system synthesized from a library of generic parametrized components; the analysis of a monitored hydraulic system represented as a digital twin. In both cases the quantities of interest are flowrates, water levels, and hydrodynamic forces. Methods to be Employed. The PR-RBC method incorporates several principal ingredients: component-to-system model construction, underlying "truth" finite element PDE discretization, (Petrov)-Galerkin projection, parametrized model-order reduction for both the inter-component (port) and intra-component (bubble) degrees of freedom, residual dual-norm a posteriori error estimators, hyperreduction approaches, offline-online computational decompositions, and parallel implementations. In this work the SCRBE formulation is expanded to treat nonlinear parabolic partial differential equations; also considered are hybrid FE + PRRBC approaches for problems characterized by advancing fronts or (local) complex coupled phenomena such as Fluid-Structure Interaction. Significance of Proposed Activity. The PR-RBC approach can yield computational savings of one or two orders of magnitude in both the "library" and "digital twin" frameworks. Riverine flows constitute an ambitious goal by which to motivate, develop, and assess the PR-RBC approach for nonlinear parabolic problems. However, the underlying technical challenges are fundamental - related to approximation theory, error estimation, and computational methodology- and the problems and disciplines to which the resulting PR-RBC techniques can be applied is very broad. Collaboration: This project will be undertaken in collaboration with the group of Dr Chris Kees of ERDC-RDE-CHL-MS.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Feb 14, 2019
- Source ID
- W911NF1910098
Entities
People
- Anthony Patera
Organizations
- Army Contracting Command
- Massachusetts Institute of Technology
- United States Army