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.
Keywords: Linearized Green-Naghdi system, absorbing boundary conditions, convolution quadrature, Padé approximation; fast algorithm, convergence analysis
@article{M2AN_2022__56_5_1687_0,
author = {Pang, Gang and Ji, Songsong and Antoine, Xavier},
title = {A fast second-order discretization scheme for the linearized {Green-Naghdi} system with absorbing boundary conditions},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {1687--1714},
year = {2022},
publisher = {EDP-Sciences},
volume = {56},
number = {5},
doi = {10.1051/m2an/2022051},
mrnumber = {4454159},
zbl = {1498.76062},
language = {en},
url = {https://www.numdam.org/articles/10.1051/m2an/2022051/}
}
TY - JOUR AU - Pang, Gang AU - Ji, Songsong AU - Antoine, Xavier TI - A fast second-order discretization scheme for the linearized Green-Naghdi system with absorbing boundary conditions JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2022 SP - 1687 EP - 1714 VL - 56 IS - 5 PB - EDP-Sciences UR - https://www.numdam.org/articles/10.1051/m2an/2022051/ DO - 10.1051/m2an/2022051 LA - en ID - M2AN_2022__56_5_1687_0 ER -
%0 Journal Article %A Pang, Gang %A Ji, Songsong %A Antoine, Xavier %T A fast second-order discretization scheme for the linearized Green-Naghdi system with absorbing boundary conditions %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2022 %P 1687-1714 %V 56 %N 5 %I EDP-Sciences %U https://www.numdam.org/articles/10.1051/m2an/2022051/ %R 10.1051/m2an/2022051 %G en %F M2AN_2022__56_5_1687_0
Pang, Gang; Ji, Songsong; Antoine, Xavier. A fast second-order discretization scheme for the linearized Green-Naghdi system with absorbing boundary conditions. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 56 (2022) no. 5, pp. 1687-1714. doi: 10.1051/m2an/2022051
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