Model Reduction for Free-Surface Flows

Abstract:

Accurate resolution of free-surface flows in natural systems usually requires characterization of the system's bathymetry and
the impact of bottom stress induced by surface roughness. Unfortunately, constants like Manning's n in common parameterizations
of bottom stress are not directly measurable, while in situ measurement of bathymetry can be expensive and impractical in many environments.
This leads to the need to solve one or more inverse problems to estimate depths and/or roughness parameters using available data, which may be limited to surface velocities and/or free-surface elevations. While a variety of techniques can be used to solve the resulting inverse problem, many involve a sampling step that can be expected to require a large number of forward simulations for real systems.

Here, we consider model reduction for free-surface flows based on Galerkin projection on a global basis provided by Proper Orthogonal
Decomposition (POD). To achieve realistic speedup, we evaluate alternative hyper-reduction methods for non-polynomial nonlinearities that arise in standard formulations. We evaluate the schemes' performance by considering their accuracy, robustness, and speed for a variety of hydrodynamic regimes in the context of both forward simulation and sampling strategies for inverse problems.