Abstract
SUMMARYWe extend the framework of the finite volume method to dispersive unidirectional water wave propagation in one space dimension. In particular, we consider a KdV–BBM‐type equation. Explicit and implicit–explicit Runge–Kutta‐type methods are used for time discretizations. The fully discrete schemes are validated by direct comparisons to analytic solutions. Invariants' conservation properties are also studied. Main applications include important nonlinear phenomena such as dispersive shock wave formation, solitary waves, and their various interactions. Copyright © 2012 John Wiley & Sons, Ltd.
Highlights
Water wave modeling is a complicated process and usually leads to models which are hard to analyze mathematically as well as to solve numerically
In this paper we study the application of some finite volume schemes to a scalar nonlinear dispersive partial differential equation modeling unidirectional wave propagation
The main scope of the present article is to extend the framework of finite volume methods to scalar unidirectional dispersive models
Summary
Water wave modeling is a complicated process and usually leads to models which are hard to analyze mathematically as well as to solve numerically. A wide range of numerical methods have been employed to compute approximate solutions to dispersive wave equations of KdV-BBM type : finite difference schemes [10, 50], finite element methods [9, 33, 2] and spectral methods [38, 39, 15, 35]. In order to apply the finite volume method to the KdV-BBM equation (1.1), we rewrite it in a conservative form, including a nontrivial evolution operator, an advective and a dispersive flux functions. Strong Stability Preserving Runge-Kutta (SSP-RK) methods, which preserve the TVD property of the finite volume scheme, [44, 24] are used for the explicit discretization.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: International Journal for Numerical Methods in Fluids
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
