Numerical modeling of Boussinesq equations by finite element method

In this paper, a numerical model based on the improved Boussinesq equations derived by Beji and Nadaoka [Beji, S., Nadaoka, K., 1996. A formal derivation and numerical modeling of the improved Boussinesq equations for varying depth. Ocean Eng. 23 (8), 691-704] is presented. The finite element method is used to discretize the spatial derivatives. Quadrilateral elements with Linear interpolating functions are employed for the two horizontal velocity components and the water surface elevation. The time integration is performed using the Adams-Bashforth-Moulton predictor-corrector method. Five test cases for which either theoretical solutions or laboratory results are available are employed to test the proposed scheme. The model is capable of giving satisfactory predictions in all cases. (C) 1999 Elsevier Science B.V. All rights reserved.