Numerical modelling of tsunami mitigation by mangroves
Putu Harry Gunawan
LAMA (Laboratoire d’Analyse et de Mathmatiques Appliques) UPEM
putu-harry.gunawan@univ.paris-est.fr
Abstract
Figure 1: Mangrove-Tsunami Model.
The role of mangroves (coastal forests) in the mitigation of tsunami impacts is a debated
topic and numerical simulation can bring an important contribution to this debate. Several
articles have been devoted to the numerical modelling of tsunami mitigation by mangroves in
the past few years [4, 2, 1, 5]. The arrival of a tsunami in a coastal area is generally described
by the shallow water model. A way of modelling the mangrove resistance is to add a bottom
friction term (similar to those used in the simulation of overland flows [3]) to the shallow water
equations:
∂t h + ∂x (hu) = 0,
∂t (hu) + ∂x
(0.1)
hu2 + 1/2gh2 + gh(∂x z + Sf ) = 0,
(0.2)
where h is the water height, u is the velocity, g is the gravitational constant, z is the topography
of the bottom, and Sf is a friction term due to the mangrove. A usual friction term is, for
instance, the so-called Manning friction:
Sf = Cf
u|u|
,
h4/3
(0.3)
where Cf is a given coefficient.
Another way of modelling the mangrove resistance is to consider the trees of the mangrove as
structures and to take into account the drag and inertial forces they induce (using the Morison
equation for instance).
The first aim of this research axis is to investigate further the modelling of tsunami mitigation by mangroves, by comparing the different approaches to describe the mangrove resistance,
by incorporating the damage of the mangrove, and by replacing the standard shallow water
model by the shear shallow water model. The second aim is to design robust and accurate
numerical schemes for this new model with source terms.
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References
[1] H.L. Koh, et all, Simulation of Andaman 2004 tsunami for assessing impact on
Malaysia, Journal of Asian Earth Sciences 36 (74-83), 2009.
[2] H. Yanagisawa et all, The reduction effects of mangrove forest on a tsunami based on
field surveys at Pakarang Cape, Thailand and numerical analysis, Estuarine, Coastal and
Shelf Science 81 (27-37), 2009.
[3] O. Delestre, Simulation du ruissellement d’eau de pluie sur des suface agricoles, PhD
thesis, Université D’orléans. 2010.
[4] S.R. Pudjaprasetya, Modeling and Simulation of Waves in Three-Layer Porous Breakwaters, submitted to Nonlinear Processes in Geophys.
[5] S.Y. Teh et all, Analytical and numerical simulation of tsunami mitigation by mangroves in Penang, Malaysia, Journal of Asean Earth Sciences, pp. 38-46, 2009.
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