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In the present paper, a novel numerical model based on the finite volume method is established to predict a time‐dependent, one‐dimensional, advection‐diffusion equation with variable coefficients in a semi‐infinite domain. The third‐and fifth‐order schemes are employed to solve the above‐mentioned equation. Totally, two dispersion problems are used to simulate various conditions as follows: (i) solute dispersion along steady flow through inhomogeneous domain and (ii) solute dispersion along temporally dependent unsteady flow through inhomogeneous domain. The inhomogeneity of the domain is provided by spatially dependent flow. The uniform node distribution is considered to divide the problem domain into a collection of smaller parts. Analytical solutions proposed in the literature are employed to demonstrate the accuracy and reliability of the suggested model. Meanwhile, the results of the aforementioned approaches are compared with the performance of the quadratic upstream interpolation for convective kinetics scheme. Lastly, the accuracy of the implemented schemes in developed model are discussed and evaluated.

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In recent years, many researchers have suggested various numerical techniques to solve the engineering problems like fluid flow intricacies. The objective of this paper is to introduce a numerical approach to simulate treatment of incompressible fluid flow in two-dimensional unsteady flow with the shallow water equations system. The governing equations were solved by Finite Volume Method in explicit conditions. Moreover, to discretize the governing equations, total variation diminishing scheme was employed in the unstructured triangular grid systems, directly. For evaluating the numerical results of developed model, the Flow3D software was used. In this direction, two hypothetical cases have been developed to investigate the accuracy of the results of the suggested model by Flow3D software. The comparison between numerical results of developed model and simulations of Flow3D software, shows good agreement. Furthermore, the suggested model can obtain acceptable results with less number of meshes than Flow3D software.

A multi-segment sharp-crested V-notch weir (SCVW) was used both theoretically and experimentally in this study to evaluate the length of the hydraulic jump at the downstream of the weir. For this aim, a SCVW with three triangular segments at different tail-water depths (tailgate angles), and ten different discharges at a steady flow condition were investigated. Then, the most effective parameters on the length of the hydraulic jump are defined and several parametric and nonparametric regression models, namely multi-linear regression (MLR), additive non-linear regression (ANLR), multiplicative non-linear regression (MNLR), and generalized regression neural network (GRNN) models are compared with two semi-empirical regression models from the literature. The results indicate that the GRNN model is the best model among the selected models. These results are also linked to the nature of the hydraulic jump and the turbulent behavior of the phenomenon, which masks the experimental results with outliers.

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