Abstract
We 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.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 717-736 |
| Number of pages | 20 |
| Journal | INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS |
| Volume | 71 |
| Issue number | 6 |
| DOIs | |
| State | Published - Feb 28 2013 |
| Externally published | Yes |
Keywords
- Finite volume method
- Nonlinear dispersive waves
- Solitary waves
- Unidirectional propagation
- Water waves
ASJC Scopus subject areas
- Computational Mechanics
- Mechanics of Materials
- Mechanical Engineering
- Computer Science Applications
- Applied Mathematics