Seismic-generated unsteady motions in shallow basins and channels. Part II: Numerical modelling

Abstract

• Seismic-generated unsteady motions are modelled by the 2D depth-averaged shallow water equations. • The numerical solution is obtained by a Godunov-type shock-capturing finite volume scheme. • Numerical tests of sloshing motion are carried out and numerical results are compared with analytical solutions. • A sensitivity analysis is performed on the influential parameters. • The numerical model is validated against experimental data and two examples of field-scale applications to real reservoirs are presented. In this paper, unsteady motions generated by seismic-type excitation are simulated by a 2D depth-averaged mathematical model based on the classic shallow water approximation. A suitable time-dependent forcing term is added in the governing equations, and these are solved by a MUSCL-type shock-capturing finite volume scheme with a splitting treatment of the source term. The HLL approximate Riemann solver is used to estimate the numerical fluxes. The accuracy of the numerical scheme is assessed by comparison with novel exact solutions of test cases concerning sinusoidally-generated sloshing in a prismatic tank, a rectangular open channel, and a parabolic basin. A sensitivity analysis is performed on the influence of the relevant dimensionless parameters . Moreover, numerical results are validated against experimental data available in literature concerning shallow water sloshing in a swaying tank. Finally, real‐scale applications to a reservoir created by a dam and an urban water-supply storage tank are presented. The results show that the model provides accurate solutions of the shallow water equations with a seismic-type source term and can be effectively adopted to predict the main flow features of the unsteady motion induced by horizontal seismic acceleration when the long wave assumption is valid.