Dissipation processes in global scale tide simulations using a high order discontinuous Galerkin model

Coastal flooding is a major risk factor for human activities located at the coast. Between the different flooding types that can occur, coastal flooding by overflowing is the one that causes the more devastating effects, because it involves the largest volumes of water. This type of flooding occurs when the mean sea water level exceeds that of coastal defenses. The sea water level at the coast is the result of tide-surge interactions (if the wave setup is neglected), which will also experience the effects of climate change and sea level rise in the coming years.

The numerical modelling is a fundamental tool to understand the phenomena involved, study the coastal hazard and prevent the risk. In this work, whose final aim is to study tide-surge interactions at the global scale, we first focus on the numerical simulation of the dissipative mechanisms, which play a central role in tide propagation. 
Indeed, numerical dissipation is added to the physical one in numerical simulations impacting the quality of the results, especially at the coast. In this context, we present a tool for the understanding of physical and numerical dissipative processes and their impacts on the tide propagation. In a barotropic framework, which is suitable to simulate the tide (and later the surge) at the global scale, we solve the non linear shallow water equations using the Uhaina model [1, 2]. It uses an arbitrary high-order discontinuous Galerkin (DG) finite elements method, which provides great parallel scaling properties (HPC). The model works on spherical geometry and includes the bathymetry, the bottom friction, the Coriolis force and the meteorological forcing (wind and atmospherical pressure). Furthermore, the model uses an artificial viscosity mechanism based on the shock capuring theory to stabilize the simulations.

In this work we improve the existing model to account for tidal effects. They include the tide generating potential, the self-attraction and loading term and the internal tide dissipation. As a first step, we show the validation of our global barotropic tidal simulations against the FES2014 model, propagating the M2 constituent of the tide by means of an unstructured mesh discretization of the globe. We then investigate global energetic and dissipative diagnosis, at different DG orders and mesh resolutions, to quantify and localize the spurious energy dissipation induced by the scheme in order to highlight the physical one (generated by bottom friction and internal tide dissipation). 

This work is carried out within the framework of the LAGOON - LArge scale Global storm surge simulation Of OceaNs - project (partnership between the French reshearching institutes BRGM, INRIA and UPPA). The project will end up by investigate the impact of future climate on tide and storm surges interactions to produce a sea level database using the Uhaina model.

[1] Filippini, A., et al. (2024). An operational discontinuous galerkin shallow water model for coastal flood assessment. Ocean Modelling, 192:102447.

[2] Arpaia, L., et al. (2022). An efficient covariant frame for the spherical shallow water equations: Well balanced dg approximation and application to tsunami and storm surge. Ocean Modelling, 169:101915