Computation of flow in open-channel transitions

The supercritical flow in open-channel transitions often produces discontinuities in the flow variables. Depending on the size, shape and kind of channels, the flow can generate normal/oblique shock waves, expansion waves, hydraulic jumps and sometimes complex wave patterns due to multiple reflection of the waves at the boundary and their subsequent interactions with one another. In the numerical simulation of these flows, uniform grid distribution may introduce detrimental effects in the prediction and resolution of the flow details. The use of the presently available numerical schemes to solve these problems on a uniformly spaced grid systems fail to resolve the characteristic flow features and hence do a poor job in simulating the flows. In this paper, MacCormack second-order accurate explicit predictor-corrector scheme is used to solve the two-dimensional depth averaged shallow water equations to numerically simulate the supercritical free-surface flows in open-channel transitions. However, instead of a fixed grid, an adaptive grid system which adjusts itself as the solution evolves is used for a better resolution of the flow properties. In the present approach, Rai and Anderson's method based on grid speed is used for grid adaptation. In a flow with shock, best solutions are obtained when the coordinate axes are aligned along the shock. Rai and Anderson's method to cluster the grids are found to fulfill this criteria and thus produces better quality solutions, as compared to those obtained with uniformly distributed grid with a specified number of grid points.