V.O.Gorban, I.M.Gorban Numerical models of non-stationary river processes |
Applied hydromechanics, Vol. 15 (87) ¹ 4, (2013) |
| The numerical algorithm for solving the system of shallow water equations is developed on the base of a Godunov-type central-upwind scheme. It uses Kurganov-Noelle-Petrova (KNP) numerical flux method, when local propagation speeds are applied for estimation of fluxes of conservative variables across control volume boundaries. This method is simultaneously well-balanced and fluid depth positivity preserving due to using special quadrature for approximation of the bottom function. Anti-diffusion term as proposed by Kurganov-Lin is applied to reduce the scheme numerical dissipation. The algorithm is tested with various examples of non-stationary hydraulic flows, including dam-break problems as in one-dimensional as in two-dimensional cases. Comparisons between numerical and exact solutions or experimental data demonstrated that the developed numerical scheme is capable of accurately reproducing various open channel flows, including subcritical, supercritical and transcritical flows. The scheme was applied for calculating velocities and water levels in the Dnieper River near Kyiv in different conditions connected as with seasonal variations of discharge as with anthropogenic loads. |
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KEY WORDS: shallow water equations, piecewise approximation, non-stationary hydraulic flows |
| TEXT LANGUAGE: Ukrainian |