Numerical Method For Tsunami Calculation Using Full Navier -Stokes Equations And The Volume Of Fluid Method

Abstract

A two-dimensional numerical model was developed to study tsunami wave generation, propagation and runup. The model is based on solving the Navier-Stokes (NS) equations. The free-surface motion is tracked using the Volume of Fluid technique. The finite difference two-step projection method is used to solve NS equations and the forward time difference method to discretize the time derivative. A structured mesh is used to discretize the spatial domain. The model has been conceived as a versatile, efficient and practical numerical tool for tsunami computation, which could address a comprehensive understanding of tsunami physics with the ultimate aim of mitigating tsunami hazards. The prediction capability of tsunami generation, propagation and runup is improved by including more accurately the effects of vertical velocity/acceleration, dispersion and wave breaking. The model has the capability to represent complex curved boundaries within a Cartesian grid system and to deal with arbitrary transient-deformed moving boundaries. The numerical model was validated using laboratory experiments and analytical solutions. The model was used as a tool to determine the adequacy of the shallow water (SW) approximation in the application of tsunami simulations. Numerical results were compared with experimental data, analytical solutions and SW results in terms of the time-history free surface elevations and velocity. Reasonable agreements were observed based on the spatial and temporal distributions of the free surface and velocity.