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Comparison Between Different Methods to Compute the Numerical Fluctuations in Path-Conservative Schemes for SWE-Exner Model

Author(s): Francesco Carraro; Valerio Caleffi; Alessandro Valiani

Linked Author(s): Alessandro Valiani

Keywords: No keywords

Abstract: We consider the Shallow Water Equations (SWE) coupled with the Exner equation. To solve these balance laws, we implement a P 0 P 2 -ADER scheme using a path conservative method for handling the non-conservative terms of the system. In this framework we present a comparison between three different Dumbser-Osher-Toro (DOT) Riemann solvers. In particular, we focus on three different approaches to obtain the eigensystem of the Jacobian matrix needed to compute the fluctuations at the cell edges. For a general formulation of the bedload transport flux, we compute eigenvalues and eigenvectors numerically, analytically and using an approximate original solution for lowland rivers (i.e. with Froude number Fr 1) based on a perturbative analysis. To test these different approaches we use a suitable set of test cases. Three of them are presented here: a test with a smooth analytical solution, a Riemann problem with analytical solution and a test in which the Froude number approaches unity. Finally, a computational costs analysis shows that, even if the approximate DOT is the most computationally efficient, the analytical DOT is more robust with about 10%of additional cost. The numerical DOT is shown to be the heavier solution.

DOI:

Year: 2016

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