Modeling and Computations of Shallow-Water Coastal Flows

Discontinuous Galerkin Methods for Sediment Transport and Hurricane Storm Surge

Clint Dawson

The University of Texas at Austin

Storm surge due to hurricanes and tropical storms results in loss of life, destruction of property, and can alter the landscape of coastal regions. Storm surge is driven primarily by wind but can also be influenced by wind-driven surface waves. Accurate computer models of storm surge should account for the coupling of wind forcing, wave radiation stresses and circulation. In addition, the entrainment and deposition of sediment during such extreme events is of interest. In this talk, we will discuss recently developed shallow water circulation/sediment transport models based on discontinuous Galerkin formulations. DG methods are well-suited for these coastal engineering applications, as they can model highly advective flows on unstructured grids, are locally mass conservative, can allow for adaptivity in both hh and p and are highly parallelizable on HPC platforms. We will describe specific modifications to the method required to handle flows through complex coastal environments, including wetting and drying, novel types of boundary conditions needed to handle overtopping of levees, and coupling with bed morphology models for modeling the transport of sediment as bed load. We will present recent applications of the DG method to storm surge modeling and sediment transport. Recent hurricanes which have struck the U.S. Gulf Coast, including Hurricane Ike, are being studied as test beds. We will compare results of these studies with data recently collected and with ``operational'' storm surge models. We will also study the effects of p-adaptivity on the model results. Furthermore, we will present results for coupling of hydrodynamics with bed morphology. The performance of the code on multi-core parallel systems with tens of thousands of cores will be discussed.