Time–Space Decoupled Explicit Method for Fast Numerical Simulation of Tsunami Propagation

This study presents a novel explicit numerical scheme for simulating tsunami propagation using the exact solution of the wave equations. The objective of this study is to develop a fast and stable numerical scheme by decoupling the wave equation in both the time and space domains. First, the finite difference scheme of the shallow-water equations for tsunami simulation are briefly introduced. The time–space decoupled explicit method based on the exact solution of the wave equation is given for the simulation of tsunami propagation without including frequency dispersive effects. Then, to consider wave dispersion, the second-order accurate numerical scheme to solve the shallow-water equations, which mimics the physical frequency dispersion with numerical dispersion, is derived. Lastly, the computation efficiency and the accuracy of the two types of numerical schemes are investigated by the 2004 Indonesia tsunami and the solution of the Boussinesq equation for a tsunami with Gaussian hump over both uniform and varying water depths. The simulation results indicate that the proposed numerical scheme can achieve a fast and stable tsunami propagation simulation while maintaining computation accuracy.