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A fast second-order discretization scheme for the linearized Green-Naghdi system with absorbing boundary conditions

Authors :
Pang, Gang
Ji, Songsong
Antoine, Xavier
Beihang University (BUAA)
College of Engineering [Beijing]
Peking University [Beijing]
Systems with physical heterogeneities : inverse problems, numerical simulation, control and stabilization (SPHINX)
Inria Nancy - Grand Est
Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)
Institut Élie Cartan de Lorraine (IECL)
Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS)
This research is partially supported by NSFC under grant Nos.11502028.
Research conducted within the context of the Sino-French International Associated Laboratory for Applied Mathematics-LIASFMA.
X. Antoine thanks the LIASFMA funding support of the Université de Lorraine.
Source :
ESAIM: Mathematical Modelling and Numerical Analysis, ESAIM: Mathematical Modelling and Numerical Analysis, 2022, 56 (5), pp.1687-1714. ⟨10.1051/m2an/2022051⟩
Publication Year :
2022
Publisher :
EDP Sciences, 2022.

Abstract

International audience; 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.

Details

ISSN :
28047214, 28227840, 0764583X, and 12903841
Volume :
56
Database :
OpenAIRE
Journal :
ESAIM: Mathematical Modelling and Numerical Analysis
Accession number :
edsair.doi.dedup.....48bc561a609b0f114ff0c074fe7e5527
Full Text :
https://doi.org/10.1051/m2an/2022051