Abstract
A new numerical scheme to solve a water flow with a free water surface and arbitrary curved ground surface is proposed. In the proposed method, by using a soroban grid system proposed by one of the authors, computational mesh is reconstruct easily at each time step so that some grid points locate on a free water surface exactly. Time development of velocity components and water surface are calculated according to an incompressible inviscid flow equation without any transformation of the equation. Advection effects are calculated by direct interpolation of the CIP method in 3rd order accuracy in spatial. After the advection is solved, acceleration of velocity components due to the pressure gradient is solved using a FDM approach on a soroban grid system. The proposed method is applied to some problems and computational results are examined through comparisons with results of other FDM scheme and theoretical result.
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