P.D. Minev, F.N. VAN De Vosse, L.J.P. Timmermans and A.A. Van Steenhoven
A splitting technique for solutions of the Navier—Stokes and the energyequations, in Boussinesq approximately, is presented. The equations are firstintegrated in time using a…
Abstract
A splitting technique for solutions of the Navier—Stokes and the energy equations, in Boussinesq approximately, is presented. The equations are first integrated in time using a splitting procedure and then discretized spatially by means of a high‐order spectral element method. The whole technique is validated on the flow in a differentially‐heated cavity at intermediate and transitional Rayliegh numbers. The results are in a very good agreement with other available numerical solutions.
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The purpose of this paper is to propose an efficient/robust numerical algorithm for solving the two‐dimensional laminar mixed‐convection in a lid‐driven cavity using the mixed…
Abstract
Purpose
The purpose of this paper is to propose an efficient/robust numerical algorithm for solving the two‐dimensional laminar mixed‐convection in a lid‐driven cavity using the mixed finite element (FE) technique.
Design/methodology/approach
A numerical algorithm was based on the so‐called consistent splitting scheme, which improved the numerical accuracy of the primitive variables. In order to obtain a stable solution, two choices of mixed FEs, the Taylor‐Hood and Crouzeix‐Raviart types, were used. Two mesh layouts were considered; uniform and non‐uniform.
Findings
To verify that the proposed scheme had a second‐order accuracy, some numerical results are presented and compared with the known solution. The answer was confirmative. Numerically accurate solutions were obtained for a fixed Prandtl number, Pr=0.71, for a range of the Reynolds number, Re from 100 to 3,000, and for a range of the Richardson number, Ri from 0.001 to 100. The results from these calculations, using the mixed FE consistent splitting scheme, agreed with the existing ones.
Research limitations/implications
Further extensions of this work could include the influence of various choices of Reynolds numbers, Prandtl numbers and Richardson numbers, and the effect of aspect ratio.
Originality/value
The present work was the first to apply a mixed FE in association with the consistent splitting scheme to the mixed convection problem.
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Aldo Tralli and Paolo Gaudenzi
To present a numerical method for the solution of the unsteady incompressible Navier‐Stokes equations in a generic setting.
Abstract
Purpose
To present a numerical method for the solution of the unsteady incompressible Navier‐Stokes equations in a generic setting.
Design/methodology/approach
The equations are discretized in space by the finite element method, and in time by a semi‐implicit finite difference scheme, using a fractional‐step method to enforce incompressibility.
Findings
The presented results demonstrate the satisfactory accuracy of the method in the simulation of vortical flows in laminar regime and the stability of the solution in presence of a strong boundary layer.
Originality/value
The successful integration of the CFD into the industrial design depends on its capability to produce accurate and reliable simulations of real life applications. These considerations drive the development of the proposed method: it can be used in conjunction with finite elements of any order of accuracy, providing accurate and numerically stable results for complex flows. Moreover, the computational requirements are low when compared with other similar strategies.
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H. J. P. Timmermans and E. Hato
In this chapter, we address the question if and how modern technology can be used to design questionnaires, diaries, web sites, and experiments to improve the validity of…
Abstract
In this chapter, we address the question if and how modern technology can be used to design questionnaires, diaries, web sites, and experiments to improve the validity of reliability of active data collection instruments. In particular, it discusses the history of computer-assisted activity diary data, reenactment sessions, stated preference methods, and interactive computer experiments with a special focus on the design of these instruments in terms of respondent support and user interfaces. Empirical evidence and experience suggests that although fascinating instruments may increase respondent motivation and involvement and therefore improve the reliability of the measurements, there is also the danger that respondents' answers are influenced by features of the electronic instrument that are not essential, reducing validity and reliability.
Soora Rasouli and Harry Timmermans
This chapter reviews models of decision-making and choice under conditions of certainty. It allows readers to position the contribution of the other chapters in this book in the…
Abstract
Purpose
This chapter reviews models of decision-making and choice under conditions of certainty. It allows readers to position the contribution of the other chapters in this book in the historical development of the topic area.
Theory
Bounded rationality is defined in terms of a strategy to simplify the decision-making process. Based on this definition, different models are reviewed. These models have assumed that individuals simplify the decision-making process by considering a subset of attributes, and/or a subset of choice alternatives and/or by disregarding small differences between attribute differences.
Findings
A body of empirical evidence has accumulated showing that under some circumstances the principle of bounded rationality better explains observed choices than the principle of utility maximization. Differences in predictive performance with utility-maximizing models are however small.
Originality and value
The chapter provides a detailed account of the different models, based on the principle of bounded rationality, that have been suggested over the years in travel behaviour analysis. The potential relevance of these models is articulated, model specifications are discussed and a selection of empirical evidence is presented. Aspects of an agenda of future research are identified.
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The chapter outlines the principles underlying relative utility models, discusses the results of empirical applications and critically assesses the usefulness of this…
Abstract
Purpose
The chapter outlines the principles underlying relative utility models, discusses the results of empirical applications and critically assesses the usefulness of this specification against commonly used random utility models and other context dependence models. It also discusses how relative utility can be viewed as a generalisation of context dependency.
Theory
In contrast to the conventional concept of random utility, relative utility assumes that decision-makers derive utility from their choices relative to some threshold(s) or reference points. Relative utility models thus systematically specify the utility against such thresholds or reference points.
Findings
Examples in the chapter show that relative utility model perform well in comparison to conventional utility-maximising models in some circumstances.
Originality and value
Examples of relative utility models are rare in transportation research. The chapter shows that several recent models can be viewed as special cases of relative utility models.
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Increasing evidence suggests that choice behaviour in real world may be guided by principles of bounded rationality as opposed to typically assumed fully rational behaviour, based…
Abstract
Purpose
Increasing evidence suggests that choice behaviour in real world may be guided by principles of bounded rationality as opposed to typically assumed fully rational behaviour, based on the principle of utility-maximization. Under such circumstances, conventional rational choice models cannot capture the decision processes. The purpose of the chapter is to propose a modeling framework that can capture both decision outcome and decision process.
Methodology
The modeling framework incorporates a discrete cognitive representation structure and implies several decision heuristics, such as conjunctive, disjunctive and lexicographic rules. This allows modeling unobserved decision heterogeneity involved in a single decision, for example, in the form of a latent-class specification, taking into account mental effort, risk perception and expected outcome as explanatory factors.
Findings
Two models based on this framework are applied to decision problems underlying pedestrian shopping behaviour and compared with conventional multinomial logit models. The results show that the proposed models may not be superior to logit models in terms of model selection criteria due to the extra complexity in selecting heuristics, but suggest more interesting insights to the underlying decision mechanisms.
Research implications
Understanding decision processes additional to outcomes is a promising research direction. A more developed model should take into account more contextual and socio-demographic factors in the heuristic selection part. The assumptions of information processing must be subject to empirical tests to validate the model.
Originality
The proposed modeling framework bridges the long-existing contradicting approaches in the field of decision modeling, namely the rational approach and the bounded rational approach, by proving that non-compensatory decision heuristics can be inferred from compensatory model formulations with discretized information representations and decision criteria assumed. It also incorporates a heuristic choice part into the decision processes in the form of latent-class specifications and shows the viability of the new modeling framework.