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: email@example.com
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
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