Time-space decoupled model with a variable-coefficient dispersive condition to simulate tsunamis over slowly varying topography

In this study, a new numerical scheme with variable-coefficient dispersive conditions was developed to simulate tsunamis over slowly varying topography. The new model was developed using a novel time-space decoupled numerical scheme that used the classic wave equation. By adapting this model to simulate tsunamis, a variable-coefficient dispersive condition was derived to consider the dispersive effects using a numerical truncation error from the numerical scheme. The stability condition and range of the variable coefficient were analyzed using a stability analysis. Using the specific dispersive condition and the modified time-space decoupled scheme, a uniform grid system can be used to simulate a dispersive tsunami over slowly varying topography. Numerical experiments for wave propagation with Gaussian humps and dipolar sources in uniform and varying topography demonstrate that the scheme is efficient for simulating tsunami propagation over slowly varying water depths with dispersive effects.