Abstract
The main motivation of this work is the implementation of a general finite element solver for some of the improved Boussinesq models. Here, we use an extension of the model proposed by Zhao et al. [2004] to investigate the behavior of surface water waves. The equations in this model do not contain spatial derivatives with an order higher than two. Some effects like energy dissipation and wave generation by natural phenomena or external physical mechanisms are also included. As a consequence, some modified dispersion relations are derived for this extended model. A matrix-based linear stability analysis of the proposed model is presented. It is shown that this model is robust with respect to instabilities related to steep bottom gradients.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Lopes, N.D., Pereira, P.J.S., Trabucho, L. (2012). Improved Boussinesq equations for surface water waves. In: Logg, A., Mardal, KA., Wells, G. (eds) Automated Solution of Differential Equations by the Finite Element Method. Lecture Notes in Computational Science and Engineering, vol 84. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23099-8_25
Download citation
DOI: https://doi.org/10.1007/978-3-642-23099-8_25
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-23098-1
Online ISBN: 978-3-642-23099-8
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)