Volume 56, Number 5, September-October 2022
|Page(s)||1687 - 1714|
|Published online||20 July 2022|
A fast second-order discretization scheme for the linearized Green-Naghdi system with absorbing boundary conditions
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: firstname.lastname@example.org
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.
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.