Numerical simulation of waves generated by a moving pressure field

Boussinesq equations with improved dispersion characteristics are employed to simulate the generation and propagation of waves due to a moving pressure field. The equations with surface pressure terms are discretized in an unconventional way so that the numerical scheme could be run in three different modes: the non-dispersive long wave mode, the classical and the improved Boussinesq mode. For a Gaussian shaped moving pressure field, the analytical solution obtained from the linearized 1-D long wave equations is used for comparisons with the numerical solutions obtained from three different modes of the scheme. A moving hemispherical pressure field and a slender ship-like pressure field are employed for 2-D numerical simulations for a range of Froude numbers. Numerically obtained wedge angles are compared with the values given by the analytical formulas of Havelock. Nonlinear simulations are also performed for visual comparisons with their linear counterparts.