Implementation of Infinite Height Levee in CaFunwave Using an Immersed Boundary Method

Numerical simulations of storm-surge-wave actions on coastal highways and levees are very important research topics for coastal Louisiana. In a large scale region hydrodynamic model, highways and levees are often complicated in geometry and much smaller in size compared to the grid size. The immersed boundary method (IBM) allows for those complicated geometries to be modeled in a less expensive way. It can allow very small geometries to be modeled in a large scale simulation, without requiring them to be explicitly on the grid. It can also allow for complicated geometries not collocated on the grid points. CaFunwave is a project that uses the Cactus Framework for modeling a solitary coastal wave impinging on a coastline, and is the wave solver in this research. The IBM allows for a levee with different geometries to be implemented on a simple Cartesian grid in the CaFunwave package. The IBM has not been used previously for this type of application. Implementing an infinite height levee using the IBM in the Cactus CaFunwave code involves introducing IB forcing terms into the standard 2-D depth averaged shallow water equation set. These forcing terms cause the 2-D solitary wave to experience a virtual force at the grid points surrounding the immersed boundary levee. In this paper the levee was implemented and tested using two different immersed boundary methods. The first method was a feedback-force method, which proved to be more effective at modeling the levee than the second method, the direct-forcing method. In this study, the results of the two methods, as well as the shape effects on the flow, are presented and discussed.