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arXiv · 1807.06908

Rigorous justification of the Favrie-Gavrilyuk approximation to the Serre-Green-Naghdi model

Vincent Duchêne
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Abstract

The (Serre-)Green-Naghdi system is a non-hydrostatic model for the propagation of surface gravity waves in the shallow-water regime. Recently , Favrie and Gavrilyuk proposed in [Nonlinearity, 30(7) (2017)] an efficient way of numerically computing approximate solutions to the Green-Naghdi system. The approximate solutions are obtained through solutions of an augmented quasilinear system of balance laws, depending on a parameter. In this work, we provide quantitative estimates showing that any regular solution of the Green-Naghdi system is the limit of solutions to the Favrie-Gavrilyuk system as the parameter goes to infinity, provided the initial data of the additional unknowns is well-chosen. The problem is therefore a singular limit related to low Mach number limits with additional difficulties stemming from the fact that both order-zero and order-one singular components are involved.

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Vincent Duchêne. 2018-07-18. Rigorous justification of the Favrie-Gavrilyuk approximation to the Serre-Green-Naghdi model. https://doi.org/10.1088/1361-6544%2Fab22fb

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