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

Abstract

Numerical simulations of stormsurge–wave actions on coastal highways and levees are very important research topics for coastal engineering. In a largescale region hydrodynamic model, highways and levees are often complicated in geometry and much smaller in size compared to the grid spacing. The immersedboundary 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 largescale 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 often used previously for these types of applications. Implementing an infiniteheight levee using the IBM into the Cactus project CaFunwave involves introducing immersedboundary (IB) forcing terms into the standard twodimensional (2D) depthaveraged shallow water equation set. These forcing terms cause the 2D solitary wave to experience a virtual force at the grid points surrounding the IB levee. In this paper, the levee was implemented and tested using two different IBMs. The first method was a feedbackforcing method, which proved to be more effective at modeling the levee than the second method, the directforcing method. In this study, the results of the two methods are presented and discussed. The effect of levee shape on the flow is also investigated and discussed in this paper.