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