Energy DISSIPATION in stepped spillways is one of the primary goals of such structures. In this study, the accuracy of the ARTIFICIAL neural network (ANNs) method, the adaptive fuzzy neural inference model method based on the trained firewall optimization algorithm (ANFIS-FA) and the gene expression programming method (GEP) in estimating the energy loss of skimming flow regime on stepped spillways has been studied. Also, by performing sensitivity analysis, the importance of input parameters in predicting energy loss for each of the three mentioned methods has been investigated. For this purpose, 154 series of laboratory data have been used. The input parameters for each method include the hydraulic jump Froude number, the Drop number, the number of steps, the pseudo bottom slope and the ratio of the critical depth to the height of each step. . The results show that all three methods had a higher ability to predict energy loss than classical methods for estimating energy loss based on conventional regression methods. The accuracy of the ANFIS-FA (with) method is slightly higher than the GEP (with) method. The accuracy of the neural network is slightly lower than the above two methods. However, the highest accuracy obtained is related to the multilayer perceptron neural network with 3 hidden layers with the number of 12, 8 and 7 nodes in each layer, respectively. In all three methods, the most effective parameter is the waterfall number and the least effective parameter is the pseudo bottom slope.

In this paper, vorticity confinement parameters are successfully developed for compressible flows. The first new confinement parameter is proportional to spectral radii of the flux Jacobian matrix. Therefore, the confinement parameter implicitly contains the local conditions of the flow field. This new method is named as lambda vorticity confinement method. In order to gain confidence in the applicability of vorticity confinement, it would be ideal to completely eliminate constant coefficients from confinement parameters. Because these constant coefficients should be determined for every problem by trial and error and it takes a long time. In the next part of this paper, a suitable relation is introduced for the vorticity confinement parameter that doesn't need any constant coefficient. This new method is named as adaptive vorticity confinement method. Then the capability of these new methods is compared with the other vorticity confinement methods for solving shock-vortex interaction and three dimensional moving vortex problems.

A stable upwind finite-difference method for unsteady gas-liquid two-phase flows is proposed and applied to shock tube flows. The ARTIFICIAL DISSIPATION terms in the flux difference splitting upwinding scheme are derived using a preconditioned matrix to enhance the stability and convergence of the numerical calculation of mixed compressible and incompressible flows with arbitrary void fractions. A homogeneous gas-liquid two-phase flow model is used. A stable four-stage Runge-Kutta method and the flux difference splitting upwind scheme combined with a third-order MUSCL TVD scheme are employed. Using the proposed method, we compute gas-liquid mixture shock tube problems and compare their results with the exact solution to check the reliability of the proposed method. Shock and expansion wave propagations through the gas-liquid two-phase media are observed in detail. The effect of the preconditioned ARTIFICIAL DISSIPATION on the numerical stability and convergence rate are investigated. We confirm that the proposed method is stable and effective for computations of unsteady two-phase complex flows with arbitrary Mach numbers.