Dispersive shallow water wave modelling. Part II: Numerical simulation on a globally flat space
Abstract
In this paper, we describe a numerical method to solve numerically the weakly dispersive fully nonlinear Serre-Green-Naghdi (SGN) celebrated model. Namely, our scheme is based on reliable finite volume methods, proven to be very effective for the hyperbolic part of equations. The particularity of our study is that we develop an adaptive numerical model using moving grids. Moreover, we use a special form of the SGN equations where non-hydrostatic part of pressure is found by solving a nonlinear elliptic equation. Moreover, this form of governing equations allows determining the natural form of boundary conditions to obtain a well-posed (numerical) problem.
Domains
Fluid mechanics [physics.class-ph] Atmospheric and Oceanic Physics [physics.ao-ph] Fluid Dynamics [physics.flu-dyn] Computational Physics [physics.comp-ph] Classical Physics [physics.class-ph] Numerical Analysis [cs.NA] Analysis of PDEs [math.AP] Numerical Analysis [math.NA] Exactly Solvable and Integrable Systems [nlin.SI] Pattern Formation and Solitons [nlin.PS]Origin | Files produced by the author(s) |
---|
Loading...