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On a conservative finite-difference method for 1D shallow water flows based on regularized equations. (English) Zbl 1356.76213
Bátkai, András (ed.) et al., Mathematical problems in meteorological modelling. Contributions based on the presentations at the workshop, Budapest, Hungary, May 2014. Cham: Springer (ISBN 978-3-319-40155-3/hbk; 978-3-319-40157-7/ebook). Mathematics in Industry 24. The European Consortium for Mathematics in Industry, 3-18 (2016).
Summary: We deal with the 1d shallow water system of equations and exploit its special parabolic regularization satisfying the energy balance law. We construct a three-point symmetric in space discretization such that the discrete energy balance law holds and check that it is well-balanced. The results of numerical experiments for the associated explicit finite-difference scheme are also given for several known tests to confirm its reliability and some advantages. The practical error behavior is also analyzed.
For the entire collection see [Zbl 1353.86002].

MSC:
76M20 Finite difference methods applied to problems in fluid mechanics
76B10 Jets and cavities, cavitation, free-streamline theory, water-entry problems, airfoil and hydrofoil theory, sloshing
65N06 Finite difference methods for boundary value problems involving PDEs
35Q35 PDEs in connection with fluid mechanics
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