Meteo-HySEA Model Equations

The system of equations implemented in Meteo-HySEA can be written as follows:

Meteo Tsunami Equations

References:

L. Arpaia, M. Ricchiuto, A. G. Filippini, and R. Pedreros, An efficient covariant frame for the spherical shallow water equations: Well balanced dg approximation and application to tsunami and storm surge, Ocean Modelling, 169 (2022), p. 101915, https://doi.org/10.1016/j.ocemod.2021.101915.

F. Bouchut, J. L. Sommer, and V. Zeitlin, Frontal geostrophic adjustment and nonlinear wave phenomena in one-dimensional rotating shallow water. part 2. high resolution numerical simulations, Journal of Fluid Mechanics, 514 (2004), pp. 35–63, https://doi.org/10.1017/s0022112004009991.

M. J. Castro, S. Ortega, and C. Parés, Well-balanced methods for the shallow water equations in spherical coordinates, Computers and Fluids, 157 (2017), pp. 196–207, https://doi.org/10.1016/j.compfluid.2017.08.035.

A. Chertock, M. Dudzinski, A. Kurganov, and M. Lukáǒvá-Medvid'ová, Well-balanced schemes for the shallow water equations with Coriolis forces, Numerische Mathematik, 138 (2017), pp. 939–973, https://doi.org/10.1007/s00211-017-0928-0.

M. Tort, T. Dubos, F. Bouchut, and V. Zeitlin, Consistent shallow-water equations on the rotating sphere with complete Coriolis force and topography, Journal of Fluid Mechanics, 748 (2014), pp. 789–821, https://doi.org/10.1017/jfm.2014.172.

I. Vilibić, Numerical simulations of the Proudman resonance, Continental Shelf Research, 28 (2008), pp. 574–581, https://doi.org/10.1016/j.csr.2007.11.005.