Fully discrete energy stability for a one-dimensional hyperbolic relaxation model with complete topography terms
Abstract
This paper concerns the design of a fully explicit, energy-stable numerical scheme for a onedimensional hyperbolic relaxation approximation of the Serre–Green–Naghdi equations over a variable bottom. The method relies on an operator splitting that decouples the model into two hyperbolic subsystems, each admitting its own exact energy balance. The first retains the shallow-water components of the equations and is referred to as the gravity part, while the second, referred to as the acoustic part, contains in particular the stiff source terms arising from the relaxation strategy. The proposed method is designed to preserve the energy balance specific to each substep at the discrete level. This yields a numerical method for strictly wet, fully nonlinear dispersive flows satisfying local discrete energy estimates for regular and possibly strongly varying topographies.
Related
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BibTeX
@misc{duran2026fully,
title = {{Fully discrete energy stability for a one-dimensional hyperbolic relaxation model with complete topography terms}},
author = {Arnaud Duran},
howpublished = {HAL},
year = {2026},
month = sep,
url = {https://hal.science/hal-05765698v1},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Fully discrete energy stability for a one-dimensional hyperbolic relaxation model with complete topography terms
AU - Arnaud Duran
PY - 2026
DA - 2026/09/26
PB - HAL
UR - https://hal.science/hal-05765698v1
AB - This paper concerns the design of a fully explicit, energy-stable numerical scheme for a onedimensional hyperbolic relaxation approximation of the Serre–Green–Naghdi equations over a variable bottom. The method relies on an operator splitting that decouples the model into two hyperbolic subsystems, each admitting its own exact energy balance. The first retains the shallow-water components of the equations and is referred to as the gravity part, while the second, referred to as the acoustic part, contains in particular the stiff source terms arising from the relaxation strategy. The proposed method is designed to preserve the energy balance specific to each substep at the discrete level. This yields a numerical method for strictly wet, fully nonlinear dispersive flows satisfying local discrete energy estimates for regular and possibly strongly varying topographies.
ER -