An Evaluation of Model Reduction Techniques for Free-Surface Flows

Modeling free-surface flows is critical to understanding a host ofenvironmental systems and physical phenomena. As a result, thereexists a rich hierarchy of mathematical formulations for flow dynamicsthat ranges in fidelity from kinematic and diffusive waveapproximations to the St Venant equations and full two-phasenon-hydrostatic approximations. Ideally, scientists and engineersshould be able to select the appropriate formulation based solely onthe physical regime and relevant quantities of interest. However,computational expense remains a barrier to the use of high-fidelityapproximations in many problems despite significant gains inalgorithmic and processor performance over the last few decades. Thisis particularly true for applications involving many queries to a flowmodel (e.g., optimal design or parameter estimation), or involverunning under limited computational resources (e.g., real-timesimulation on hand-held devices). Here we consider model reduction as a means to bring higher fidelityfree-surface flow approximations to bear in suchapplications. Specifically, we evaluate approaches based on ProperOrthogonal Decomposition and Reduced Basis methods fordepth-integrated and non-hydrostatic approximations of free-surfaceflows. We evaluate the schemes' accuracy and performance for a seriesof test problems and pay particular attention to their consistency androbustness under varying flow regimes.