A POD-based reduced order finite volume model for solving shallow water equations with parameterized source terms
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The shallow water equations (SWE) are widely used to model non-stationary free surface flows. Some important characteristics of realistic scenarios such as the bed slope and the roughness coefficient are described by considering parameter-dependent source terms. The solution of the SWE are approximated with numerical methods, but it may involve high computational costs in realistc cases (García-Navarro and Vázquez-Cendón, 2000). In this way, reduced-order models (ROMs) based on the proper orthogonal decomposition (POD) are used to save computational costs without loss of accuracy (Solán-Fustero et al., 2023). ROMs need to be trained using a set of high-fidelity solutions (or snapshots) for a given set of parameter values. For this purpose, a POD-based reduced order finite volume method for the parameterized SWE is designed and the parameters are in the source term. The main objective of this work is focused on studying the possibilities of extrapolating solutions when solving outside of the training range of parameters with different strategies (Zokagoa and Soulaïmani, 2018). The efficiency of the model is analyzed through several examples for a set of test parameter values.
