Waves in waterways generated by moving pressure field in Boussinesq equations using unstructured finite element model

Abstract

A finite element model for depth integrated form of Boussinesq equations is presented. The equations are solved on an unstructured triangular mesh using standard Galerkin method with mixed interpolation scheme. The elemental integrals are calculated analytically and time-stepping is done using Runge–Kutta 4th order method. It is extended to simulate ship-generated waves using moving pressure fields. The unstructured formulation provides the flexibility of mesh refinement as needed, for capturing wave transformation or moving pressure field. The model is verified against experimental and numerical results for wave transformation over the Whalin shoal. The results for moving pressure field are compared against numerical results from FUNWAVE. Further, a simulation of ship navigating a curved path is presented. Finally, a real-life application and validation against field measurements is provided for waves generated by a fast ferry moving along a GPS tracked path in Tallinn Bay, Estonia.