A Radial Basis Function (RBF) Method for the Fully Nonlinear 1D Serre Green-Naghdi Equations
Fluid Dynamics
2014-07-17 v1 Numerical Analysis
Abstract
In this paper, we present a spectral method based on Radial Basis Functions (RBFs) for numerically solving the fully nonlinear 1D Serre Green-Naghdi equations. The approximation uses an RBF discretization in space and finite differences in time; the full discretization is obtained by the method of lines technique. For select test cases (see Bonnenton et al. [2] and Kim [11]) the approximation achieves spectral (exponential) accuracy. Complete \textsc{matlab} code of the numerical implementation is included in this paper (the logic is easy to follow, and the code is under 100 lines).
Cite
@article{arxiv.1407.4300,
title = {A Radial Basis Function (RBF) Method for the Fully Nonlinear 1D Serre Green-Naghdi Equations},
author = {Maurice S. Fabien},
journal= {arXiv preprint arXiv:1407.4300},
year = {2014}
}
Comments
19 pages, 9 figures, 2 tables. Includes explicit Matlab code in this paper. For downloads see https://github.com/msfabien