The particle swarm optimization (PSO) method and the genetic algorithm (GA) were used to derive formulas for determining the velocity and concentration profiles in sheet flows. Specifically, these evolutionary optimization algorithms were used in conjunction with experimental data to determine coefficients and identify parameters for preselected formulas. The objective function, defined as the sum-of-squared errors between observed and predicted values of sediment velocity and concentration, was minimized by adjusting the parameter values in the formulas. Two well-known empirical formulas were also applied to the same data. The bias, root mean square error and scatter index were used to evaluate the comparison between predictions and measurements. The results indicated that the errors based on the PSO and GA approaches to predicting sediment parameters were less than those of the existing empirical formulas. Overall, both evolutionary approaches provided formulas that were in good agreement with the experimental data, giving improved descriptions of the vertical distribution of velocity and sediment concentration in the sheet flow for practical purposes. These models also described well the behavior of the velocity and sediment concentration above the sheet flow layer; in contrast with most existing formulas that are applicable only to the sheet flow layer.

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SUMMARYIn this paper, an approach to improve the application of the differential quadrature method for the solution of Navier–Stokes equations is presented. In using the conventional differential quadrature method for solving Navier–Stokes equations, difficulties such as boundary conditions' implementation, generation of an ill conditioned set of linear equations, large memory storage requirement to store data, and matrix coefficients, are usually encountered. Also, the solution of the generated set of equations takes a long running time and needs high computational efforts. An approach based on the point pressure–velocity iteration method, which is a variant of the Newton–Raphson relaxation technique, is presented to overcome these problems without losing accuracy. To verify its performance, four cases of two‐dimensional flows in single and staggered double lid‐driven cavity and flows past backward facing step and square cylinder, which have been often solved by researchers as benchmark solution, are simulated for different Reynolds numbers. The results are compared with existing solutions in the open literature. Very good agreement with low computational efforts of the approach is shown. It has been concluded that the method can be applied easily and is very time efficient. Copyright © 2012 John Wiley & Sons, Ltd.

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