# A flexible genuinely nonlinear approach for wave propagation, breaking and runup

1 CARDAMOM - Certified Adaptive discRete moDels for robust simulAtions of CoMplex flOws with Moving fronts
IMB - Institut de Mathématiques de Bordeaux, Inria Bordeaux - Sud-Ouest
Abstract : We consider a two steps solution procedure composed by: a first step where the non hydrostatic source term is recovered by inverting the elliptic coercive operator associated to the dispersive effects; a second step which involves the solution of the hyperbolic shallow water system with the source term, computed in the previous phase, which accounts for the non-hydrostatic effects. Appropriate numerical methods that can be also generalized on arbitrary unstructured meshes are used to discretize the two stages: the standard $C^0$ Galerkin finite element method for the elliptic phase; either third order Finite Volume of third order stabilized Finite Element methods for the hyperbolic phase. The discrete dispersion properties of the fully coupled schemes obtained are studied, showing accuracy close or better to that of a fourth order finite difference method. The hybrid approach of locally reverting to the nonlinear shallow water equations is used to recover energy dissipation in breaking regions. To this scope we evaluate two strategies~: simply neglecting the non-hydrostatic contribution in the hyperbolic phase~; imposing a tighter coupling of the two phases, with a wave breaking indicator embedded in the elliptic phase to smoothly turn off the dispersive effects. The discrete models obtained are thoroughly tested on benchmarks involving wave dispersion, breaking and runup, showing a very promising potential for the simulation of complex near shore wave physics in terms of accuracy and robustness.
Document type :
Reports

Cited literature [62 references]

https://hal.inria.fr/hal-01166295
Contributor : Mario Ricchiuto <>
Submitted on : Wednesday, June 24, 2015 - 2:40:48 PM
Last modification on : Monday, March 29, 2021 - 2:40:53 PM
Long-term archiving on: : Friday, May 5, 2017 - 1:28:32 PM

### File

RR8746.pdf
Files produced by the author(s)

### Identifiers

• HAL Id : hal-01166295, version 2

### Citation

Andrea Gilberto Filippini, Maria Kazolea, Mario Ricchiuto. A flexible genuinely nonlinear approach for wave propagation, breaking and runup. [Research Report] RR-8746, Inria Bordeaux Sud-Ouest; INRIA. 2015. ⟨hal-01166295v2⟩

Record views