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Lateral intakes are hydraulic structures used for domestic, agricultural and industrial water conveyance, characterized by a very complex three-dimensional morphodynamic behavior: since streamlines near the lateral intake are deflected, some vortices form, pressure gradient, shear and centrifugal forces at the intake generate flow separation and a secondary movement, responsible for local scour and sediment deposition. On the other side, the modeling of flows, besides the sediment transport, in curved channels implies some more complications in comparison with straight channels. In this research, this complex process has been investigated experimentally and numerically, with the mechanism of sediment transport, bed topography evolution, flow pattern and their interactions. Experiments were performed in the Laboratory of Tarbiat Modares University, Iran, where a U-shaped channel with a lateral intake was installed and dry sediment was injected at constant rate into a steady flow. Due to the spiral flow, the bed topography changes significantly and the bed forms in turn affect the sediment entering the intake. Different from the previous works on this topic which were mainly based on laboratory experiments, here, Computational Fluid Dynamics (CFD) numerical simulations with FLUENT software were also performed, specifically with the two-phase Eulerian Model (EM) and Discrete Phase Model (DPM), at the aim of evaluating their performance in reproducing the observed physical processes. This software is used for a large variety of CFD problems, but not much for simulating sediment transport phenomena and bed topography evolution. The comparison of the results obtained through the two models against the laboratory experimental data proved a good performance of both the models in reproducing the main features of the flow, for example, the longitudinal and vertical streamlines and the mechanism of particles movement. However, the EM reveals a better performance than DPM in the prediction of the secondary flows and, consequently, of the bed topography evolution, whereas the DPM well depicts the particles pattern, predicts the location of trapped particles and determines the percentage of sediment entering the intake.

The numerical models so calibrated and validated were applied to other cases with different positions of the intake in the bend. The results show that mechanism of sediment entrance into the intake varies in different position. If the intake is installed in the second half of the bend, the sediment accumulates along the inner bank of the bend and enters the intake from downstream edge of intake; on the other side, if it is placed in the first half of the bend, the sediment accumulates along both the inner and the outer bends and, therefore, more sediment enters the intake. Also the results of the simulations performed with the DPM model for different positions of the lateral intake show that for all discharge ratios, the position of 120^∘ is the one which guarantees the minimum ratio of sediment diverted to the intake (Gr).

In this paper, we derive the mathematical model that allows chemotaxis in avascular tumor growth in a two-phase medium. The two phases are the viscous cell phase and the inviscid fluid phase. The conservation of mass–momentum is incorporated in each phase, and appropriate constitutive laws are applied to formulate the governing equations. Further, these equations are simplified into three main variables: cell volume fraction, cell velocity, and nutrient concentration. These variables generate a coupled system of nonlinear partial differential equations. A numerical scheme based on the finite volume method is applied to approximate the solution of cell volume fraction. The finite element method is applied to approximate the solutions of cell velocity and nutrient concentration. In this research paper, we investigate tumor growth when tumor cells move along a fluid containing a diffusible nutrient to which the cells are drawn. We perform some numerical simulations to show the effect of the parameters. The findings of this literature are compatible with the existing literature.

The main purpose of this work is to study the long-time behavior of a compressible gas–liquid model based on the drift-flux formulation. The model is composed of two mass conservation equations and one mixture momentum equation. The flow domain is closed at one end and involves a free gas–liquid interface at the other where both phases vanish. The model includes a slip between the gas and liquid phases, i.e. they move with different velocities. This is a main reason why the model is useful for many industrial applications. We introduce a reformulation of the model based on the gas velocity. This gives rise to new nonlinear terms in the mixture momentum equation which account for the difference in the gas and liquid velocity. New challenges in the mathematical analysis will then appear. In particular, under appropriate smallness conditions on initial data (initial energy) various time-independent estimates of gas and liquid masses, as well as fluid velocities, are obtained. Novel upper and lower bounds on masses are provided that contain precise information about the time-dependent decay rate. Hence, the long-time behavior can be directly extracted from these estimates.

In this paper, the large time behavior of the solution to the initial-boundary problems for the one-dimensional compressible gas–liquid drift-flux model with slip is studied. Under some suitable smallness conditions upon the initial data, the optimal pointwise upper and lower decay estimates on masses as well as the sharpest decay rates for the norms in terms of the velocity function are obtained. This result generalizes the one in [On the large time behavior of the compressible gas–liquid drift-flux model with slip, Math. Models Methods Appl. Sci.25 (2015) 2175–2215] by Evje and Wen. The key of the proof is to derive some new global-in-time weighted estimates. Our method can also be easily adopted to the study on the large time behavior of the solution to the one-dimensional compressible Naiver–Stokes equations.

In this paper, a two-phase computational model of a composite (TwPM) with cylindrical inclusion of square cross-sections and small sizes is proposed. The applied asymptotic techniques devoted to the analysis of the constructed TwPM are validated through a comparison of the results reported by others. A simple analytical formula of the reduced heat transfer parameter for small size of inclusions is derived, and an asymptotic character of Maxwell Garnett (MG) formula is illustrated.

A new three-dimensional two-phase model on meso-scales for fluid-saturated porous media is proposed. Based on this model, a three-dimensional fluid-solid mixture explicit dynamic finite element scheme is developed by adopting direct coupling technique. Using Galerkin residual method and considering the coupling effects on the fluid-solid interface, the model is discrete into solid elements, fluid elements and fluid-solid coupling elements. Moreover, three-dimensional wave propagation in the fluid-saturated porous media is numerically calculated and the propagation characteristic of main waves is discussed.