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On the Galerkin/Finite-Element Method for the Serre Equations

Mitsotakis, Dimitrios ; Ilan, Boaz ; Dutykh, Denys

Journal of Scientific Computing, 2014, Vol.61(1), pp.166-195 [Tạp chí có phản biện]

ISSN: 0885-7474 ; E-ISSN: 1573-7691 ; DOI: 10.1007/s10915-014-9823-3

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  • Nhan đề:
    On the Galerkin/Finite-Element Method for the Serre Equations
  • Tác giả: Mitsotakis, Dimitrios ; Ilan, Boaz ; Dutykh, Denys
  • Chủ đề: Green–Naghdi equations ; Traveling waves ; Undular bores
  • Là 1 phần của: Journal of Scientific Computing, 2014, Vol.61(1), pp.166-195
  • Mô tả: A highly accurate numerical scheme is presented for the Serre system of partial differential equations, which models the propagation of dispersive shallow water waves in the fully-nonlinear regime. The fully-discrete scheme utilizes the Galerkin / finite-element method based on smooth periodic splines in space, and an explicit fourth-order Runge–Kutta method in time. Computations compared with exact solitary and cnoidal wave solutions show that the scheme achieves the optimal orders of accuracy in space and time. These computations also show that the stability of this scheme does not impose very restrictive conditions on the temporal stepsize. In addition, solitary, cnoidal, and dispersive shock waves are studied in detail using this numerical scheme for the Serre system and compared with the ‘classical’ Boussinesq system for small-amplitude shallow water waves. The results show that the interaction of solitary waves in the Serre system is more inelastic. The efficacy of the numerical scheme for modeling dispersive shocks is shown by comparison with asymptotic results. These results have application to the modeling of shallow water waves of intermediate or large amplitude.
  • Ngôn ngữ: English
  • Số nhận dạng: ISSN: 0885-7474 ; E-ISSN: 1573-7691 ; DOI: 10.1007/s10915-014-9823-3

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