Abstract
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.
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Acknowledgements
This work was supported by The National Research University Higher School of Economics’ Academic Fund Program, project No. 15-09-0266 and the Russian Foundation for Basic Research, project No. 13-01-00703.
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Zlotnik, A., Gavrilin, V. (2016). On a Conservative Finite-Difference Method for 1D Shallow Water Flows Based on Regularized Equations. In: Bátkai, A., Csomós, P., Faragó, I., Horányi, A., Szépszó, G. (eds) Mathematical Problems in Meteorological Modelling. Mathematics in Industry(), vol 24. Springer, Cham. https://doi.org/10.1007/978-3-319-40157-7_1
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DOI: https://doi.org/10.1007/978-3-319-40157-7_1
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