| Issue |
ESAIM: M2AN
Volume 56, Number 5, September-October 2022
|
|
|---|---|---|
| Page(s) | 1687 - 1714 | |
| DOI | https://doi.org/10.1051/m2an/2022051 | |
| Published online | 20 July 2022 | |
A fast second-order discretization scheme for the linearized Green-Naghdi system with absorbing boundary conditions
1
School of Mathematical Science, Beihang University, Beijing 100083, P.R. China
2
HEDPS, CAPT, and LTCS, College of Engineering, Peking University, Beijing 100871, P.R. China
3
Université de Lorraine, CNRS, Inria, IECL, F-54000 Nancy, France
* Corresponding author: gangpang@buaa.edu.cn
Received:
5
August
2021
Accepted:
19
May
2022
In this paper, we present a fully discrete second-order finite-difference scheme with fast evaluation of the convolution involved in the absorbing boundary conditions to solve the one-dimensional linearized Green-Naghdi system. The Padé expansion of the square-root function in the complex plane is used to implement the fast convolution. By introducing a constant damping parameter into the governing equations, the convergence analysis is developed when the damping term fulfills some conditions. In addition, the scheme is stable and leads to a highly reduced computational cost and low memory storage. A numerical example is provided to support the theoretical analysis and to illustrate the performance of the fast numerical scheme.
Mathematics Subject Classification: 76B15 / 65M06 / 65R10
Key words: Linearized Green-Naghdi system / absorbing boundary conditions / convolution quadrature / Padé approximation; fast algorithm / convergence analysis
© The authors. Published by EDP Sciences, SMAI 2022
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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