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Journal Articles ESAIM: Mathematical Modelling and Numerical Analysis Year : 2022

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

Abstract

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.
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Dates and versions

hal-03130074 , version 1 (03-02-2021)

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Cite

Gang Pang, Songsong Ji, Xavier Antoine. A fast second-order discretization scheme for the linearized Green-Naghdi system with absorbing boundary conditions. ESAIM: Mathematical Modelling and Numerical Analysis, 2022, 56 (5), pp.1687-1714. ⟨10.1051/m2an/2022051⟩. ⟨hal-03130074⟩
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