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A numerical scheme for an improved Green-Naghdi model in the Camassa-Holm regime for the propagation of internal waves. (English) Zbl 1390.76400

Summary: In this paper, we introduce a new reformulation of the Green-Naghdi model in the Camassa-Holm regime for the propagation of internal waves over a flat topography derived by V. Duchêne et al. [SIAM J. Math. Anal. 47, No. 1, 240–290 (2015; Zbl 1317.76027)]. These new Green-Naghdi systems are adapted to improve the frequency dispersion of the original model, they share the same order of precision as the standard one but have an appropriate structure which makes them much more suitable for the numerical resolution. We develop a second order splitting scheme where the hyperbolic part of the system is treated with a high-order finite volume scheme and the dispersive part is treated with a finite difference approach. Numerical simulations are then performed to validate the model and the numerical methods.

MSC:

76M12 Finite volume methods applied to problems in fluid mechanics
65M08 Finite volume methods for initial value and initial-boundary value problems involving PDEs
76B55 Internal waves for incompressible inviscid fluids
76M20 Finite difference methods applied to problems in fluid mechanics
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs

Citations:

Zbl 1317.76027

Software:

Matlab; HE-E1GODF
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References:

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