A new numerical scheme for improved Businnesque equations with surface pressure

In this work an improved Boussinesq model with a surface pressure term is discretized by a new approach. By specifying a single parameter the proposed discretization enables the user to run the program either in the long wave mode without dispersion terms or in the Boussinesq mode. Furthermore, the Boussinesq mode may be run either in the classical Boussinesq mode or in the improved Boussinesq mode by setting the dispersion parameter appropriately. In any one of these modes it is possible to specify a fixed or a moving surface pressure for simulating a moving object on the surface. The numerical model developed here is first tested by comparing the numerically simulated solitary waves with their analytical counterparts. The second test case concerns the comparison of the numerical solutions of moving surface pressures with the analytical solutions of the long wave equations for all possible modes (long wave, classical, and improved Boussinesq).