A POD-based reduced-order model for free surface shallow water flows over real bathymetries for Monte-Carlo-type applications

This paper presents a reduced-order model (ROM) to efficiently handle the uncertainties in the simulation of real free surface flows. The approach is dedicated to Monte-Carlo-type applications. The ROM is designed by projecting the non-linear shallow-water equations on a low-dimension basis, obtained using the proper orthogonal decomposition (POD) method. The non-linear terms are treated, through some specific approximations, to obtain the speedup expected from the reduced-order modeling methodology. The main motivation is the need for a faster numerical model to tackle the challenges posed by multiple-query applications such as optimal design or probabilistic analyses that use a large number of evaluations of the outputs for different values of input parameters. In the present work, the POD bases are constructed from data provided by a full-order finite volume model for a considered benchmark test with some given input parameters. This study first shows that the reduced-order model can simulate the dynamics of various dam break flows over variable bathymetries with significant speedups. A sensitivity analysis is then performed to evaluate to what extent the ROM can reproduce the dynamics of new scenarios obtained after varying the original input parameters. Good results are obtained for reasonable changes in the input parameters.