A Numerical Code for Waves in a Two-Layer Shallow Fluid

The preliminary results from a two-dimensional two-layer nonlinear shallow water model are presented. The system is composed of two inviscid, incompressible, and immiscible fluids of constant density. The waves are assumed to be nonlinear and non-dispersive and the water depth is assumed to be constant. A high order predictor-corrector algorithm with a high order finite difference discretization, accurate to O(Δx⁴) is developed. The numerical algorithm and the boundary conditions are outlined and the model is compared with the analytical solution of internal solitary waves.