Applied PDE Group
Nonlinear Partial Differential Equations in Fluid and Solid Mechanics


Finite volume methods for unidirectional dispersive wave model

D. Dutykh, Th. Katsaounis, D. Mitsotakis, Finite volume methods for unidirectional dispersive wave model, Int. J. for Num. Methods in Fluids, 71(6): 717-736,  2013​​​​
D. Dutykh, Th. Katsaounis, D. Mitsotakis
finite volume method; nonlinear dispersive waves; unidirectional propagation; solitary waves; water waves
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 applica- tions include important nonlinear phenomena such as dispersive shock wave formation, solitary waves, and their various interactions.