Riadh Ata

Finite volume schemes and residual distribution schemes for pollutant transport on unstructured grids

In this work, a recent residual distribution scheme and a second-order finite volume method are compared to model the transport of a pollutant in free surface flows. The phenomenon is described in two dimensions using the shallow water (SW) system augmented by a scalar conservation law for the pollutant transport. The two numerical methods are developed to minimize the numerical diffusion which is a critical problem for transport phenomena. The conservation of the mass and the monotonicity of the solution are two other important numerical requirements necessary to reproduce the physics of the problem. These three features (low numerical diffusion—mass conservation—monotonicity) will be theoretically analyzed and then numerically verified through a series of test cases. Both methods are used on completely unstructured grids, but the regularity of the grid with respect to the streamlines direction produces for the two methods different behaviours which will be studied. This work has been realized within the Telemac-2D system, constituted by a finite element kernel and a finite volume kernel. Telemac2D uses several numerical schemes, including the new schemes presented here. The aim of this paper is to present state-of-the-art research in the field of finite volumes (FV) and of residual distribution schemes for advection problems.

Variational Data Assimilation With Telemac. Proof Of Concept For Model State Correction On The Berre Lagoon 3D-Model

TELEMAC is a component of the open-source integrated suite of solvers TELEMAC-MASCARET for use in the field of free-surface flow that solves the Reynolds Averaged Navier-Stokes equations. Generally speaking, uncertainties in the model formulation itself due to simplified physics and also in the input fields to the model such as the boundary conditions, initial conditions and hydraulic parameters translate into errors in the simulated hydraulic variables. In spite of significant advances in numerical schemes, description of geographical data (topography, bathymetry) and environmental conditions (hydrologycal and meteorological fields), the representation of the true state of a system as well as its forecasted state remains imperfect and some of these limits can be overcome combining observations with simulation via data assimilation techniques. This paper presents the implementation of a 3D-Var FGAT variational data assimilation algorithm as a proof of concept for improving TELEMAC simulations and forecast. The demonstration is made on the Berre lagoon application with TELEMAC-3D: the salinity state is sequentially corrected assimilating in situ salinity measurements.

Uncertainty Quantification for River Flow Simulation Applied to a Real Test Case: The Garonne Valley

Sensitivity analysis techniques have been widely used in multitude of applications to quantify the impact of inputs variables imprecision on the accuracy of the model output variables. Depending on the problem at hand, an appropriate method of sensitivity analysis should be selected. Direct and adjoint sensitivity analysis are two complementary approaches known to be efficient. While the direct approach provides an assessment of the propagation of the error of a given input parameter in the studied system, the adjoint approach enables to identify the source of the uncertainty of a given output variable with respect to several input parameters. Direct methods have been extensively investigated in different geophysical applications, particularly in the context of the hydraulic modeling. In this work, several methods will be described and applied to the same benchmark during over-flooding events. The effect of uncertainties in the boundary conditions, the spatially distributed functions (bed level, river width, friction, etc.) and the numerical parameters on the model state variables (discharge, water surface elevation, etc.) is examined. This study has been carried out on the Garonne River test case, along a 50 km downstream reach, using 1D full Saint-Venant hydraulic models SIC2 (Irstea) or Mascaret (EDF), and 2D Telemac model (EDF). Results illustrate the influence of individual and combined contributions of input variables uncertainties.

Estimation of Lateral Inflows Using Data Assimilation in the Context of Real-Time Flood Forecasting for the Marne Catchment in France

The present study describes the assimilation of discharge in situ data for operational flood forecasting. The study was carried out on the Marne River (France) catchment where lateral inflows’ uncertainty is important due to karstic areas. This source of error was partly accounted for using an Extended Kalman Filter (EKF) algorithm built on the top of a mono-dimensional hydraulic model. The lateral inflows were sequentially adjusted over a sliding 48 h time window. The correction leads to a significant improvement in the simulated water level and discharge in re-analysis and forecast modes. These results pave the way for the operational use of the data assimilation (DA) procedure for real-time forecasting at the French flood forecasting service.