Solution of the hyperbolic mild-slope equation using the finite volume method

A finite volume solver for the 2D depth-integrated harmonic hyperbolic formulation of the mild-slope equation for wave propagation is presented and discussed. The solver is implemented on unstructured triangular meshes and the solution methodology is based upon a Godunov-type second-order finite volume scheme, whereby the numerical fluxes are computed using Roeʹs flux function. The eigensystem of the mild-slope equations is derived and used for the construction of Roeʹs matrix. A formulation that updates the unknown variables in time implicitly is presented, which produces a more accurate and reliable scheme than hitherto available. Boundary conditions for different types of boundaries are also derived. The agreement of the computed results with analytical results for a range of wave propagation/transformation problems is very good, and the model is found to be virtually paraxiality-free.