Chercheur doctorant: Louis Goffin

Promoteur: Prof. Michel Pirotton

Contributions to uncertainty analysis of computational models with application to hydrodynamics and physically-based hydrological simulations.


Modelling numerically natural phenomena like river flows, flows on hydraulic structures or groundwater flows, helps engineers quantifying them in order to organise human activities on the one hand and design mitigation measures on the other hand. These models take, as input data, quantities that are uncertain because of their variability in time and space, and because of our lack of knowledge to represent them accurately. Uncertainty analysis aims at quantifying the impact of these uncertain input data on the outputs of the model.

Several uncertainty analysis methods exist, including the well-known Monte Carlo method (MCM). However, it requires to evaluate the numerical model many times, which is not compatible with computationally expensive 2-D hydrodynamic models for instance. Other uncertainty analysis methods (Point Estimates Method (PEM), Perturbance Moment Method (PMM) and Stochastic Response Surface Method (SRSM)), based on simplifying assumptions, allow to decrease significantly the number of model evaluations. Non-hydraulic simple tests performed with these methods showed that they produce very good results compared to MCM.

In order to consider testing and challenging these methods on more computationally expensive examples, a fast and robust 1-D steady shallow water model is developed. It includes an original sliding domain strategy used along with the nonlinear Krylov accelerator. After a validation step on academic tests, this new model showed an excellent scalability behaviour. Compared to CasADi, a state-of-the-art optimization tool, the new model produced better performance results.

This new model allows to apply MCM to a real world 1-D shallow water case. The assessment of the flooding risk of a field located on the banks of the Haine River in Belgium is done through MCM, PEM and PMM. PMM showed in this example to produce an excellent compromise between the computation cost and the accuracy. Moreover, results were very close to the ones produced by MCM.
After this successful hydraulic application for PMM, this method is applied to a 2-D horizontal shallow water flow in the Romanche River in the French Alps. Thanks to an uncertainty analysis approach, this emblematic example studies the sediment transport potential after several dam removals. Results reflect an increased sediment movement potential after dam removal even if the uncertainty analysis highlights a relatively wide confidence interval on the amount of sediments transported.

Over the needs for fast computing models for the application to hydrodynamics, the automatic run of an uncertainty analysis requires also robust models. Groundwater partially saturated models can present convergence issues as reported in the scientific literature. In this thesis, a chapter tries to tackle this problem by proposing a promising method. Homotopy is tested and gives encouraging results in terms of convergence rate.




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