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The purpose of this paper is twofold. Firstly, to present a detailed account of the generalized Lagrangian formulation of Hui and Zhao, in which the stream function ζ and Lagrangian distance λ, are used as independent variables, and secondly to assess and compare the performance of various flux limiters in this formulation with their corresponding performance in the Eulerian formulation. The generalized Lagrangian formulation is obtained by a transformation from the cartesian co‐ordinates (x, y) to the Lagrangian co‐ordinates (λ, ζ). In this manner, the number of independent variables for steady, 3‐D flow is reduced from four to three, placing this formulation on the same footing as the Eulerian formulation even for steady flows (as opposed to the conventional Lagrangian formulation which apparently still requires four independent variables even for steady flows). The generalized Lagrangian formulation with the Godunov scheme (using flux limiters) appears to have distinct advantages over the corresponding Eulerian formulation, particularly with respect to accuracy. Furthermore, the method requires no grid generation.

The purpose of this paper is to apply the variational multi-scale framework to the finite element approximation of the compressible Navier-Stokes equations written in conservation form. Even though this formulation is relatively well known, some particular features that have been applied with great success in other flow problems are incorporated.

The orthogonal subgrid scales, the non-linear tracking of these subscales, and their time evolution are applied. Moreover, a systematic way to design the matrix of algorithmic parameters from the perspective of a Fourier analysis is given, and the adjoint of the non-linear operator including the volumetric part of the convective term is defined. Because the subgrid stabilization method works in the streamline direction, an anisotropic shock capturing method that keeps the diffusion unaltered in the direction of the streamlines, but modifies the crosswind diffusion is implemented. The artificial shock capturing diffusivity is calculated by using the orthogonal projection onto the finite element space of the gradient of the solution, instead of the common residual definition. Temporal derivatives are integrated in an explicit fashion.

Subsonic and supersonic numerical experiments show that including the orthogonal, dynamic, and the non-linear subscales improve the accuracy of the compressible formulation. The non-linearity introduced by the anisotropic shock capturing method has less effect in the convergence behavior to the steady state.

A complete investigation of the stabilized formulation of the compressible problem is addressed.

The viscous finite volume lambda formulation is presented. The suggested technique is apt to compute viscous flows with heat fluxes. The inviscid terms are evaluated by means of the non‐conservative, very accurate upwind methodology, known as the finite volume lambda formulation. The diffusive terms, on the contrary, are approximated by a central scheme. Both methods are characterized by a nominal second order accuracy in space. Efficiency is enhanced by means of a multigrid technique which directly combines each grid level with each stage of an explicit multistage time integration technique. A laminar viscous flow about a NACA 0012 airfoil and a turbulent one about a RAE 2822 airfoil have been computed as well as the two‐ and three‐dimensional turbulent flows inside the Stanitz elbow. The computed numerical results are in very good agreement with well assessed published numerical or experimental results. The suggested multigrid technique allows significant work reductions for laminar as well as for turbulent flow computations.

The modelling of steady‐state natural and mixed convection in obstructed channels is presented. The two‐dimensional numerical analysis is carried out with a finite element thermally coupled incompressible flow formulation written in terms of the primitive variables of the problem and solved via a generalized streamline operator technique. Natural convection is studied in several vertical channel configurations for a wide range of Rayleigh numbers while mixed convection is analysed in a horizontal channel with a built‐in rectangular cylinder for different Reynolds and Grashof numbers. The results obtained in this work are validated with available experiments and other existing numerical solutions.

The purpose of this paper is twofold: first to carry out a comprehensive literature review for state of the art regarding airline schedule planning and second to identify some new research directions that might help academic researchers and practitioners.

The authors mainly focus on the research work appeared in the last three decades. The search process was conducted in database searches using four keywords: “Flight scheduling,” “Fleet assignment,” “Aircraft maintenance routing” (AMR), and “Crew scheduling”. Moreover, the combination of the keywords was used to find the integrated models. Any duplications due to database variety and the articles that were written in non-English language were discarded.

The authors studied 106 research papers and categorized them into five categories. In addition, according to the model features, subcategories were further identified. Moreover, after discussing up-to-date research work, the authors suggested some future directions in order to contribute to the existing literature.

The presented categories and subcategories were based on the model characteristics rather than the model formulation and solution methodology that are commonly used in the literature. One advantage of this classification is that it might help scholars to deeply understand the main variation between the models. On the other hand, identifying future research opportunities should help academic researchers and practitioners to develop new models and improve the performance of the existing models.

This study proposed some considerations in order to enhance the efficiency of the schedule planning process practically, for example, using the dynamic Stackelberg game strategy for market competition in flight scheduling, considering re-fleeting mechanism under heterogeneous fleet for fleet assignment, and considering the stochastic departure and arrival times for AMR.

In the literature, all the review papers focused only on one category of the five categories. Then, this category was classified according to the model formulation and solution methodology. However, in this work, the authors attempted to propose a comprehensive review for all categories for the first time and develop new classifications for each category. The proposed classifications are hence novel and significant.

The centrifugal instability mechanism of boundary layers over concave surfaces is responsible for the development of quasi-periodic, counter-rotating vortices aligned in a streamwise direction known as Görtler vortices. By distorting the boundary layer structure in both the spanwise and the wall-normal directions, Görtler vortices may modify heat transfer rates. The purpose of this study is to conduct spatial numerical simulation experiments based on a vorticity–velocity formulation of the incompressible Navier–Stokes system of equations to quantify the role of the transition in the heat transfer process.

Experiments are conducted using an in-house, parallel, message-passing code. Compact finite difference approximations and a spectral method are used to approximate spatial derivatives. A fourth-order Runge–Kutta method is adopted for time integration. The Poisson equation is solved using a geometric multigrid method.

Results show that the numerical method can capture the physics of transitional flows over concave geometries. They also show that the heat transfer rates in the late stages of the transition may be greater than those for either laminar or turbulent ones.

The numerical method can be considered as a robust alternative to investigate heat transfer properties in transitional boundary layer flows over concave surfaces.

The purpose of this paper is to show the superior turbulence method in CFD analysis of radial turbo machines and to introduce the best way to choose turbulence parameters whenever FLUENT user applies this software as a complementary design tool for high‐speed turbo machinery components.

One of the most important issues in CFD is analysis of flow field in turbo machines. Flow in high‐speed radial turbo machinery is a 3D, turbulent and unsteady behavior so needs suitable method for converging. It is clear that the turbulence model has an extraordinary effect on investigation of 3D flows in high‐speed turbo machinery. A centrifugal compressor of micro and radial turbines have been designed and simulated 3D using the commercial CFD‐code FLUENT 6. Three turbulence models k‐ε/standard, renormalization‐group (RNG) and RSM were considered and results of three models were compared with experimental and 1D design results.

The study showed numerical results are compatible with experimental performance data. It determined that RNG method in CFD analysis of radial turbo machines has provided better results than the standard k‐ε method. In addition, when using the RNG method, the phenomena of flow field were more visible than other methods.

This paper offers use of the RNG method as a superior turbulence method in CFD analysis of radial turbo machines.

The value chain of the Norwegian meat production industry has recently been through major structural changes resulting in increased flows and transportation needs at all levels. The purpose of this paper is to present results of the initial stage of a five‐year research project between the Norwegian Meat Research Centre, Norwegian meat companies and Molde University College. The main goal of the project is to develop a decision support system for the transport of live animals to a slaughterhouse to reduce transportation costs while maintaining high level of livestock welfare and meat quality, as these are three main factors for the profitability of both farmers and industry.

The paper presents a mixed integer programming model that combines vehicle routing and inventory control. We introduce the possibility for multiple routes for a given vehicle on a given day in a multiple‐period planning perspective. Arrival times of the loaded vehicles to the slaughterhouse are controlled by production (slaughter) rate and inventory level at the abattoirs so that the supply of animals for slaughter is steady and production breaks are avoided. Livestock welfare is secured by the route duration constraints.

The model has been formulated and tested on small data sets. The major future challenge is to solve real‐life problems from the involved companies.

The main limitation is the present inability to solve large cases.

The model combining transportation and inventory control in a setting of animal welfare constraints is original.

Beijing rail transit can actively control the density of rail transit passenger flow, ensure travel facilities and provide a safe and comfortable riding atmosphere for rail transit passengers during the epidemic. The purpose of this paper is to efficiently monitor the flow of rail passengers, the first method is to regulate the flow of passengers by means of a coordinated connection between the stations of the railway line; the second method is to objectively distribute the inbound traffic quotas between stations to achieve the aim of accurate and reasonable control according to the actual number of people entering the station.

This paper analyzes the rules of rail transit passenger flow and updates the passenger flow prediction model in time according to the characteristics of passenger flow during the epidemic to solve the above-mentioned problems. Big data system analysis restores and refines the time and space distribution of the finely expected passenger flow and the train service plan of each route. Get information on the passenger travel chain from arriving, boarding, transferring, getting off and leaving, as well as the full load rate of each train.

A series of digital flow control models, based on the time and space composition of passengers on trains with congested sections, has been designed and developed to scientifically calculate the number of passengers entering the station and provide an operational basis for operating companies to accurately control flow.

This study can analyze the section where the highest full load occurs, the composition of passengers in this section and when and where passengers board the train, based on the measured train full load rate data. Then, this paper combines the full load rate control index to perform reverse deduction to calculate the inbound volume time-sharing indicators of each station and redistribute the time-sharing indicators for each station according to the actual situation of the inbound volume of each line during the epidemic. Finally, form the specified full load rate index digital time-sharing passenger flow control scheme.

This study aims to provide a solution of the power flow calculation for the low-voltage ditrect current power grid. The direct current (DC) power grid is becoming a reliable and economic alternative to millions of residential loads. The power flow (PF) in the DC network has some similarities with the alternative current case, but there are important differences that deserve to be further concerned. Moreover, the dispatchable distributed generators (DGs) in DC network can realize the flexible voltage control based on droop-control or virtual impedance-based methods. Thus, DC PF problems are still required to further study, such as hosting all load types and different DGs.

The DC power analysis was explored in this paper, and an improved Newton–Raphson based linear PF method has been proposed. Considering that constant impedance (CR), constant current (CI) and constant power (CP) (ZIP) loads can get close to the practical load level, ZIP load has been merged into the linear PF method. Moreover, DGs are much common and can be easily connected to the DC grid, so V nodes and the dispatchable DG units with droop control have been further taken into account in the proposed method.

The performance and advantages of the proposed method are investigated based on the results of the various test systems. The two existing linear models were used to compare with the proposed linear method. The numerical results demonstrate enough accuracy, strong robustness and high computational efficiency of the proposed linear method even in the heavily-loaded conditions and with 10 times the line resistances.

The conductance corresponding to each constant resistance load and the equivalent conductance for the dispatchable unit can be directly merged into the self-conductance (diagonal component) of the conductance matrix. The constant current loads and the injection powers from dispatchable DG units can be treated as the current sources in the proposed method. All of those make the PF model much clear and simple. It is capable of offering enough accuracy level, and it is suitable for applications in DC networks that require a large number of repeated PF calculations to optimize the energy flows under different scenarios.