One-equation Model Research Articles

Strategies for Enhancing One-Equation Turbulence Model Predictions Using Gene-Expression Programming

This paper introduces innovative approaches to enhance and develop one-equation RANS models using gene-expression programming. Two distinct strategies are explored: overcoming the limitations of the Boussinesq hypothesis and formulating a novel one-equation turbulence model that can accurately predict a wide range of turbulent wall-bounded flows. A comparative analysis of these strategies highlights their potential for advancing RANS modeling capabilities. The study employs a single-case CFD-driven machine learning framework, demonstrating that machine-informed models significantly improve predictive accuracy, especially when baseline RANS predictions diverge from established benchmarks. Using existing training data, symbolic regression provides valuable insights into the underlying physics by eliminating ineffective strategies. This highlights the broader significance of machine learning beyond developing turbulence closures for specific cases.

Infection spreading in tissue as a reaction-diffusion wave.

Viral infection develops in the organism due to virus replication inside infected cells and its transmission from infected to uninfected cells through the extracellular matrix or cell junctions. In this work, we model infection spreading in tissue with a delay reaction-diffusion system of equations for the concentrations of uninfected cells, infected cells and virus. We prove the wave existence, determine its speed of propagation and introduce a simplified one-equation model obtained from the complete model using a quasi-stationary approximation.

Conjugate Heat Transfer Advancements and Applications in Aerospace Engine Technology

Over the past few decades, conjugate heat transfer (CHT) technology has been instrumental in predicting temperature fields within aerospace engines, guiding engine design with its predictive capabilities. This paper comprehensively surveys the foundational technologies of CHT and their applications in engine design, backed by an extensive literature review. A novel coupling iteration methodology, su-F-TFTB, was proposed. Following this, it introduced grid splicing technology tailored for heat flux conservation, which significantly enhances the adaptability of CHT grids. Ultimately, this study employed the self-developed Aerospace Engine Numerical Simulation (AENS v4.0.1) software to perform CHT analyses on NASA-C3X turbine blades equipped with ten radial cooling systems. A comparative analysis of pressure distributions across various density meshes was undertaken to affirm mesh independence. Furthermore, the impacts of the Spalart–Allmaras (SA) one-equation model and k–ω Shear Stress Transport (SST) two-equation model on the temperature distribution in conjugate heat transfer were investigated. The results indicated that the k–ω SST model exhibited superior performance, aligning closely with NASA experimental data. This validation confirmed the effectiveness of the software.

Computational study of magneto-convective flow of aqueous-Fe3O4 nanoliquid in a tilted cylindrical chamber partially layered by porous medium: Entropy generation analysis

In various industrial applications, the main objective is to enhance thermal efficiency by minimizing the generation of entropy. Specifically, achieving optimal thermal efficiency in a tilted cylindrical chamber poses significant challenges due to the combined effects of tangential and normal gravity components. Our study focuses on the flow dynamics, thermal transport, and entropy generation of Fe3O4/H2O nanoliquid within a cylindrical annular enclosure by incorporating the synergistic effects of magnetic force, geometric inclination angle, and thickness of the porous region. The Brinkman–Forchheimer-extended Darcy model for ferrofluid motion and the one-equation model for heat transfer are applied in the porous region, while the conventional Navier–Stokes and energy equations are used in the fluid-only region. A series of computations is performed for various key parameters, such as Hartmann number (0≤Ha≤60), Darcy number (10−5≤Da≤10−1), porous layer thickness (0.1≤ε≤0.9), and angle of inclination (−60°≤γ≤60°). Our results reveal that the heat transport rate is enhanced by 48.6% with an increase in the Darcy number from 10−5 to 10−1. Moreover, the flow circulation and heat transport can be optimized by tilting the enclosure anticlockwise. It has been found that 91.8% of flow strength can be enhanced by rotating the enclosure from −60° to 60°. Finally, this study suggests that the inclination angle of 30° and a porous layer thickness of 0.3 emerge as the ideal configuration to obtain optimal performance, particularly for lower Hartmann and higher Darcy numbers. Our findings will provide insight into optimizing thermal processes in nanoliquid-filled enclosures subjected to magnetic force.

Towards the understanding of vortex breakdown for improved RANS turbulence modeling

A triple-delta wing configuration in transonic conditions has been investigated numerically, explicitly focusing on the leading-edge vortices during sideslip flow. Several shock waves manifest over the fuselage, leading to vortex-shock interactions. The primary focus of the analysis centers on the vortex breakdown phenomenon and its underlying causes. The flow field obtained from different turbulence modeling approaches is compared. This study aims to identify the limitations of a standard one-equation model in dealing with such complex applications. It explores physical and modeling reasons leading to the model's inaccuracies. The impact of turbulence treatment on the numerical results is explored, discussing turbulence-related variables. A novel and straightforward modification to the one-equation turbulence model is then introduced and assessed compared to experimental and computational data. The proposed model appears promising for enhancing the accuracy of the one-equation Reynolds Averaged Navier-Stokes outcomes.

Local thermal equilibrium constraints for energy transport equations for thermal oil recovery processes

The mathematical framework of reservoir thermal simulators typically relies on the assumption of local thermal equilibrium (LTE) when modeling energy transport through porous media for petroleum engineering applications, including Thermal Enhanced Oil Recovery (TEOR) processes. The LTE presupposes instantaneous exchange of energy between the injected hot fluids and the reservoir's rock and fluids. Nevertheless, it is essential to acknowledge that LTE's validity becomes questionable in specific scenarios, potentially resulting in an overestimation of oil recovery, e.g., when high fluid velocities arise. Under such conditions, the local thermal non-equilibrium (LTNE) formulation may offer a more accurate representation of the energy transport physics. In this study, we present the physical constraints that must be satisfied for the application of two distinct mathematical formulations (1) the one-equation model for the fluids and rock as a whole (LTE is assumed), and (2) the two-equation model, one equation assigned to the fluids and another one to the rock (pseudo-LTNE is assumed). Such constraints were derived by examining conductive and convective heat transport properties via the theory of the method of volume averaging, specifically applied to an oil-water-gas-rock system at the pore scale. It was found that the one-equation model requires that 18 physical constraints to be satisfied, while the pseudo-LTNE model needs to fulfill 9 physical constraints. A sensitivity analysis was conducted based on factor upon which accumulation, conduction and convection constraint equations depend, aiming to identify the conditions under which LTNE occurs within the porous medium. These influencing factors encompass the characteristic time, the Peclet number, the presence of external heat sources, the distribution of phases at the pore-scale, and the disparity between rock and fluid properties. The combinations of these factors can induce the existence of local thermal non-equilibrium. One significant property is the heat transfer coefficient in the reservoir. We recommend that the pseudo-LTNE approach is reliable as long as the rock-fluid heat transfer coefficients are at least one order of magnitude larger than the fluid-fluid heat transfer coefficients (1000−10000W/(m3K)). Contrarily, the OEM should be employed only when the heat transfer coefficients surpass a threshold value of 10000W/(m3K). When injector and producer wells are hydraulically interconnected, resulting in heightened fluid velocities, it is encouraged the use of the two-equations model. The predictability and reliability of the energy models were verified by comparison of predicted oil recovery against data from laboratory experiments. The equations presented in this study consistently demonstrate their utility in assessing the reliability of energy transport models for TEOR scenarios.

Implementation, Realization and an Effective Solver of Two-Equation Turbulence Models

Currently, when the Reynolds-Averaged Navier–Stokes (RANS) equations are solved using turbulence modelling, most often the one-equation model of Spalart and Allmaras is used. Then, it is only necessary to solve the RANS equations in conjunction with a single transport equation for modeling turbulence. For this model, considerable assessment and analysis has been performed, allowing the possibility of a reliable solution method for an eddy viscosity required to compute the Reynolds stresses in the RANS equations. Such evaluation along with analysis has not been performed for similar performance with two-equation models of the k\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$k$$\\end{document}-ω\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\omega $$\\end{document} type. The primary objective of this paper is to present and discuss the components of an effective numerical algorithm for solving the RANS equations and the two transport equations of k\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$k$$\\end{document}-ω\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\omega $$\\end{document} type turbulence models. All the important details of the turbulence model as actually implemented are given, which is sometimes not done in various papers considering such modeling. The viability and effectiveness of this solution algorithm are demonstrated by solving both two-dimensional and three-dimensional aerodynamic flows. In all applications, a linear rate of convergence without oscillations or other evidence of unstable behavior is observed. This behavior is also particularly true when the proposed algorithm is applied to systematically refined mesh sequences, which is generally not observed with algorithms solving more than one transport equation. Thus numerical integration errors are systematically reduced, allowing for a significantly more reliable assessment of the effectiveness of the model itself. Additionally, in this paper analysis of the solution algorithm, including linear stability, is also performed for a particular flow problem.

Entropy generation in local non-similar dissipative MHD flow of CH3OH + Fe3O4 and C12H26-C15H32 + Fe3O4 ferrofluids

This analysis examines the local non-similar flow of two nanofluids with base fluids (methanol and kerosene oil) containing magnetite nanoparticles. Comparison between heat transfer characteristics is performed by incorporating viscous and ohmic heating. The flow is induced by a linear vertically stretching surface, and corresponding governing boundary layer equations do not admit the similarity solutions because the mixed convection parameter is not free from the streamwise coordinate. Therefore, the local non-similarity approach is implemented, and solutions are obtained by using the two-equation model. Graphs are displayed to investigate the impacts of dimensionless parameters on velocity profile, temperature distribution, entropy generation and the Bejan number. The linear regression model is applied to investigate the rate of growth/decrease of the skin friction coefficient and Nusselt's number with growing values of physical parameters. Values of the skin-friction coefficient and Nusselt’s number are also obtained from the first level of truncation (one-equation model) and the second level of truncation (two-equation model). Comparative analysis reveals that relative error between the numerical values obtained from the first and second levels of truncation is an increasing function of the transformed streamwise coordinate.

Large eddy simulation of plunging solitary wave: Understanding the breaking and turbulent mechanisms along shoaling region

A large eddy simulation (LES) is conducted to investigate the distribution of turbulence kinetic energy (TKE) under a plunging solitary wave over a 1:15 slope. This study provides a novel contribution to the field by examining the roles of resolved and sub-grid scale TKE in plunging solitary waves at the different stages of wave breaking. Furthermore, comparing the performances of two sub-grid scale (SGS) models in simulating the distribution of TKE was carried out to identify their performances. The separate investigation of these components in the context of wave breaking and recognizing the importance of an appropriate sub-grid scale model to consider the effects of small-scale eddies provide a significant advancement in understanding coastal morphological changes and nearshore sediment transport. Both the zero-equation and one-equation SGS models demonstrated acceptable performance in simulating water surface and kinematic properties. The one-equation SGS model, however, provided more accurate results on TKE transport during the breaking process and as the wave approaches its collapsing point. The study’s results reveal that an SGS model’s inability to simulate TKE transport (such as in the zero equation model) leads to inaccurate simulations of the TKE level and breaking location in the breaking zone. Additionally, the results of the one-equation model demonstrated that the maximum horizontal fluid velocity around the wavefront surface is a better predictor of breaking wave onset than the horizontal fluid velocity at the wave crest.

Nonhydrostatic simulation of internal lee wave-induced turbulence mixing: A comparative study of second-moment closure mixing schemes for an idealized marginal sea sill topography

To further understand the processes of wave-turbulence interactions under nonhydrostatic conditions and to gain insight into the selection of second-moment closure models in subsequent nonhydrostatic ocean models, a newly developed nonhydrostatic ocean model is coupled with the General Ocean Turbulence Model (GOTM) to form a robust version of the Marine Environment Research and Forecasting Model (MERF). On this basis, internal lee wave simulation with various turbulent mixing schemes is investigated for an idealized two-dimensional supercritical sea slope topography with high-resolution (100 m). First, the LES-type simulation based on a 3D Smagorinsky diffusivity scheme can reproduce well the characteristics of lee waves, serving as a benchmark for comparison. Second, the Mellor and Yamada (MY) scheme and the quasi-equilibrium scheme are able to effectively simulate the effects of internal waves on large-scale structures, while small-scale dynamic processes are partially suppressed by turbulent mixing. However, the K-ε model and the one-equation model further suppress the small-scale dynamic processes and weaken the propagation of internal lee waves due to overly strong turbulence mixing. Finally, the generation of a lee wave changes the instantaneous temperature field, and the use of the second-moment closure models converts more energy into irreversible mixing. Enhancing the model resolution can slightly improve the accuracy of the simulation in exchange for paying considerable computation.

Quantitative investigation of the turbulence model effect on high-pressure-ratio centrifugal compressor performance prediction

The accuracy of centrifugal compressors performance and flow field prediction by Computational Fluid Dynamics (CFD) is a serious problem facing in the design and analysis process due to its complex flow feature inside. Different turbulence models choosing in the Reynolds-Averaged Navier-Stokes Equations (RANS) leads to different simulation results. In this paper, a high-pressure-ratio centrifugal compressor was used as the simulation object to discuss the effect of common turbulence models, including a one-equation model (Spalart-Allmaras model), a two-equation linear model (Shear Stress Transport model) and a two-equation nonlinear model (Explicit Algebraic RSM model), on performance prediction under design speed. By introducing the calculation method of local entropy generation rate, an improved method of dividing different types of loss in centrifugal compressors was proposed. After comparing with the experiment results, the effect of turbulence models on loss prediction inside the compressor was quantitative investigated. Further, the flow mechanism underlying was discussed. The results show that the secondary flow loss have the largest impact on the components' prediction performance, also, the reasons for different magnitudes of secondary flow loss inside the impeller and the diffuser are different. These comparisons hope to help designers choose an appropriate turbulence model in further compressor design process and may benefit future turbulence modelling development.

Hyperbolic equivalent k-ϵ and k-ω turbulence models for moment-closures

The ten-moment equations are considered as a first-order alternative of Navier-Stokes equations when the effect of heat transfer is negligible. This model takes the form of first-order hyperbolic conservation laws, which carry many numerical advantages. However, the applicability of this model is still limited due to the lack of appropriate turbulence models. Applying the Reynolds-averaging concept to the ten-moment model, a set of governing equations for turbulent flow can be obtained, which is referred to as the Reynolds-averaged ten-moment equations. The traditional turbulence models designed for the Reynolds-averaged Navier-Stokes (RANS) equations are not ideal for the Reynolds-averaged ten-moment equations, as the extra partial differential equations (PDEs) introduce second-order derivatives. These terms destroy the pure hyperbolic nature of the original system of equations, which consequently removes all numerical advantages of first-order systems. To maintain the first-order hyperbolic form, the desired turbulence model should remain in the same form. Recently, a hyperbolic-relaxation turbulence model has been proposed by the authors, which is developed by hyperbolizing Prandtl's one-equation model using a relaxation method known as the Chen-Levermore-Liu p-system. Unfortunately, developing a hyperbolic version of two-equation models using the same method is very difficult. This is because the diffusion coefficients of the two-equation models are more complicated than in the one-equation model. In this paper, another relaxation method, the Cattaneo-Vernotte approach, is used to develop the hyperbolic-relaxation form of classical two-equation models. The solution of the resulting equations exhibits dispersive wave behaviour. To study this feature, a dispersion analysis of the Reynolds-averaged ten-moment equations with the new turbulence models is presented. Several numerical experiments are studied to investigate the effect of the relaxation parameters. The derived turbulence models are then coupled to the Reynolds-averaged ten-moment equation and further validated by solving a canonical two-dimensional turbulent plane mixing-layer problem, planar free-jet problem, and circular free-jet problem.

Simulations of Hypersonic Boundary-Layer Transition over a Flat Plate with the Spalart-Allmaras One-Equation BCM Transitional Model

Transitional flow has a significant impact on vehicles operating at supersonic and hypersonic speeds. An economic way to simulate this problem is to use computational fluid dynamics (CFD) codes. However, not all CFD codes can solve transitional flows. This paper examines the ability of the Spalart–Allmaras one-equation BCM (SA-BCM) transitional model to solve hypersonic transitional flow, implemented in the open-source CFD code Eilmer. Its performance is validated via existing wind tunnel data. Eight different hypersonic flow conditions are applied. A flat plate model is built for the numerical tests. The results indicate that the existing SA-BCM model is sensitive to the freestream turbulence intensity and the grid size. It is not accurate in all the test cases, though the transitional length can be matched by tuning the freestream intensity. This is likely due to the intermittency term of the SA-BCM model not being appropriately calibrated for high-velocity flow, though if the model can be recalibrated it may be able to solve the general high-velocity flows. Although the current SA-BCM model is only accurate under certain flow conditions after one calibration process, it remains attractive to CFD applications. As a one-equation model, the SA-BCM model runs much faster than multiple-equation flow models.

Finite time blow-up for some parabolic systems arising in turbulence theory

We study a class of non-linear parabolic systems relevant in turbulence theory. Those systems can be viewed as simplified versions of the Prandtl one-equation and Kolmogorov two-equation models of turbulence. We restrict our attention to the case of one space dimension. We consider initial data for which the diffusion coefficients may vanish. We prove that, under this condition, those systems are locally well-posed in the class of Sobolev spaces of high enough regularity, but also that there exist smooth initial data for which the corresponding solutions blow up in finite time. We are able to put in evidence two different types of blow-up mechanism. In addition, the results are extended to the case of transport-diffusion systems, namely to the case when convection is taken into account.

Uncertainty analysis of turbulence model in capturing flows involving laminarization and retransition

Flows experiencing laminarization and retransition are universal and crucial in many engineering applications. The objective of this study is to conduct an uncertainty quantification and sensitivity analysis of turbulence model closure coefficients in capturing laminarization and retransition for a rapidly contracting channel flow. Specifically, two commonly used turbulence models are considered: the Spalart-Allmaras (SA) one-equation model and the Menter Shear Stress Transport (SST) two-equation model. Thereby, a series of steady Reynolds Averaged Navier-Stokes (RANS) predictions of aero-engine intake acceleration scenarios are carried out with the purposely designed turbulence model closure coefficients. As a result, both SA and SST models fail to capture the retransition phenomenon though they achieve pretty good performance in laminarization. Using the non-intrusive polynomial chaos method, solution uncertainties in velocity, pressure, and surface friction are quantified and analyzed, which reveals that the SST model possesses much great uncertainty in the non-laminar regime, especially for the logarithmic law prediction. Besides, a sensitivity analysis is performed to identify the critical contributors to the solution uncertainty, and then the correlations between the closure coefficients and the deviations of the outputs of interest are obtained via the linear regression method. The results indicate that the diffusion-related constants are the dominant uncertainty contributors for both SA and SST models. Furthermore, the remarkably strong correlation between the critical closure coefficients and the outputs might be a good guide to recalibrate and even optimize the commonly used turbulence models.

Design-Based Research in Empirical Microeconomics

I briefly review the emergence of “ design-based” research methods in labor economics in the 1980s and early 1990s. These methods were seen as a partial solution to the problems of credible inference identified by Ashenfelter (1974), Leamer (1978), Hendry (1980), and others. Designed-based studies typically use a simplified one-equation model of the outcome of interest—in contrast to model-based studies that specify a data generating process for all factors determining the outcome. I discuss some of the strengths and weaknesses of the design-based approach and the value of such research in the field. (JEL C20, J01, J24, J31, J38, J51, J53)

Galilean-Invariant Stability-Based Transition Transport Modeling Framework

A new stability-based transition transport modeling framework for unstructured computational fluid dynamics is introduced. Based on a four-equation model published recently by the authors of this paper, new model formulations are derived being Galilean invariant and fully local. Moreover, the complexity of the four-equation model is reduced, yielding a one-equation model that is based on a local pressure-gradient parameter and a three-equation model that is based on an averaged pressure-gradient parameter considering convection (history) effects. Since the model versions are identical except the pressure-gradient parameter, the implementation effort is reduced. To be able to compute test cases in adverse pressure gradient flow regions at low Reynolds numbers, a method was developed to accelerate the turbulence production (downstream of the point of transition onset) that can also be used inside laminar separation bubbles. The models were implemented into the DLR TAU code, the unstructured compressible finite-volume flow solver of the German Aerospace Center (DLR) for external flows. For verification and validation purposes different test cases are shown capturing a wide range of parameters and flow conditions. This includes a test case verifying that the model yields identical results with and without uniform motion (Galilean invariance). Additionally, industrially relevant three-dimensional test cases were computed. This includes a helicopter rotor in vertical flight.

Long-wave instabilities of evaporating/condensing viscous film flowing down a wavy inclined wall: Interfacial phase change effect of uniform layers

The interfacial phase change effect on a thin film flowing down an undulated wall has been investigated in the present study. The study is performed for a general periodic undulated bottom of moderate steepness that is long compared to the film thickness, followed by a case study over the sinusoidal bottom. The long-wave instabilities of the ununiform film are used by deriving a nonlinear evolution equation in the classical long-wave expansion method framework. The one-equation model can track the free surface evolution and involve the bottom undulation, viscosity, gravity, surface tension, and phase change (evaporation/condensation) effects. Linear stability analysis shows that the bottom steepness ζ has a dual role. In the downhill region, increasing ζ destabilizes, whereas increasing ζ stabilizes in the uphill region. Weakly nonlinear waves are studied using the method of multiple scales to obtain the complex Ginzburg–Landau equation. The results show that both supercritical and subcritical solutions are possible for evaporating and condensate film. Interestingly, while one subcritical region is visible for an evaporating film, two subcritical unstable regions are found for condensate film. The numerical solution of the free-surface equation demonstrates the finite-amplitude behavior that tends to dry out for an evaporating film. For condensate film, the thickness increases rapidly. The rupture dynamics highly depend on the initial perturbation, and the bottom steepness has a negligible effect on it. Kutateladze number has a significant impact on the stability characteristic of the film flow as it represents a sort of efficiency of phase change that occurs at the interface.

Local correlation-based transition models for high-Reynolds-number wind-turbine airfoils

Abstract. Modern wind-turbine airfoil design requires robust performance predictions for varying thicknesses, shapes, and appropriate Reynolds numbers. The airfoils of current large offshore wind turbines operate with chord-based Reynolds numbers in the range of 3–15 million. Turbulence transition in the airfoil boundary layer is known to play an important role in the aerodynamics of these airfoils near the design operating point. While the lack of prediction of lift stall through Reynolds-averaged Navier–Stokes (RANS) computational fluid dynamics (CFD) is well known, airfoil design using CFD requires the accurate prediction of the glide ratio (L/D) in the linear portion of the lift polar. The prediction of the drag bucket and the glide ratio is greatly affected by the choice of the transition model in RANS CFD of airfoils. We present the performance of two existing local correlation-based transition models – one-equation model (γ− SA) and two-equation model (γ-Reθt‾- SA) coupled with the Spalart–Allmaras (SA) RANS turbulence model – for offshore wind-turbine airfoils operating at a high Reynolds number. We compare the predictions of the two transition models with available experimental and CFD data in the literature in the Reynolds number range of 3–15 million including the AVATAR project measurements of the DU00-W-212 airfoil. Both transition models predict a larger L/D compared to fully turbulent results at all Reynolds numbers. The two models exhibit similar behavior at Reynolds numbers around 3 million. However, at higher Reynolds numbers, the one-equation model fails to predict the natural transition behavior due to early transition onset. The two-equation transition model predicts the aerodynamic coefficients for airfoils of various thickness at higher Reynolds numbers up to 15 million more accurately compared to the one-equation model. As a result, the two-equation model predictions are more comparable to the predictions from eN transition model. However, a limitation of this model is observed at very high Reynolds numbers of around 12–15 million where the predictions are very sensitive to the inflow turbulent intensity. The combination of the two-equation transition model coupled with the Spalart–Allmaras (SA) RANS turbulence model is a good method for performance prediction of modern wind-turbine airfoils using CFD.

Spatio-temporal modelling and prediction of bus travel time using a higher-order traffic flow model

Accurate bus travel time prediction in real-time is challenging, as numerous factors such as fluctuating travel demand, incidents, signals, bus stops, dwell times, and seasonal variations can affect travel time, a spatio-temporal variable. Literature that considered the spatio-temporal evolution of bus travel time adopting traffic flow theory-based models investigated one-equation models (also widely known as first-order model) predominantly while the two-equation models (commonly known as higher-order models) have not been sufficiently explored due to their complex structure, parameters to calibrate, hardship in obtaining the data, and difficulty in discretizing and solving. Motivated by this, the present study explores the suitability of higher order traffic flow models for the prediction of bus travel time. This study adopted a well-known two-equation model ‘Aw-Rascle model‘ (Aw and Rascle, 2000), which addressed most of the limitations of the previous models, and discretized using a Finite volume method to preserve the conservational properties of Partial Differential Equations (PDE). As Global Positioning System (GPS) is a widespread data source for transit systems, the identified model was rewritten in terms of speed by adopting a suitable pressure function. The discretized model was represented in the state-state-space form and integrated with a filtering technique using appropriate inputs, to facilitate real-time implementation. The performance of the proposed methodology was evaluated and compared with a first order model (Lighthill Whittam Richards (LWR) model) based approach to understand the efficacy of the higher-order models in travel time prediction. The prediction accuracy in terms of Mean Absolute Percentage Error (MAPE) was around 14% for the proposed methodology with an absolute deviation of around +/-1.2 min, which was better than the existing LWR model-based prediction method. The developed real-time prediction methodology is a promising one to be integrated with Advanced Public Transportation Systems (APTS) applications.