High resolution flux-difference-splitting scheme on adaptive grid for open-channel flows. (Q2739233)

The authors investigate how to enhance the shock resolution by using a second-order accurate scheme for open-channel flows. The second-order accurate flux-difference-splitting (FDS) scheme based on Lax-Wendroff numerical flux for simulating one-dimensional transient free surface flows is implemented on a fixed as well as on a self-adjusting grid for examining the improvement in shock resolution. The grid-adjusting procedure, developed by \textit{A. Harten} and \textit{J. M. Hyman} [J. Comput. Phys. 50, 235--269 (1983; Zbl 0565.65049)], adjusts the grid by averaging local characteristic velocities with respect to the signal amplitude in such a way that the shock always lies at a mesh point. The \textit{P. L. Roe}'s approximate Jacobian [J. Comput. Phys. 43, 357--372 (1981; Zbl 0474.65066)] is used for conservation and consistency, while theoretically sound treatment for satisfying entropy inequality conditions ensures physically realistic solutions. Details about inclusion of source terms, treated in a way consistent with the general formulation of the FDS scheme, are explained. Numerical examples concerning complex channel flows are given to illustrate the effectiveness of the technique for handling source terms.