Kees Vuik

Delft University of Technology, Delft, South Holland, Netherlands

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Publications (37)22.8 Total impact

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    ABSTRACT: An historical overview of the development of traffic flow models is proposed in the form of a model tree. The model tree shows the genealogy of four families: the fundamental relation, microscopic, mesoscopic and macroscopic models. We discuss the families, branches and models. By describing the historical developments of traffic flow modeling, we take one step further back than conventional literature reviews that focus on the current state-of-the-art. This allows us to identify the main trends in traffic flow modeling: (1) convergence of many branches to generalized models, (2) adaptations and extensions of the LWR model to deal with real phenomena, (3) multi-class versions of many models and, (4) the development of hybrid models combining the advantages of different types of models.
    01/2014; DOI:10.1007/s13676-014-0045-5
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    ABSTRACT: We propose and analyze a generic multi-class kinematic wave traffic flow model: Fastlane. The model takes into account heterogeneity among driver-vehicle units with respect to speed and space occupancy: long vehicles with large headways (e.g. trucks) take more space than short vehicles with short headways (e.g. passenger cars). Moreover, and this is what makes the model unique, this effect is larger when the traffic volume is higher. This state dependent space occupancy is reflected in dynamic passenger car equivalent values. The resulting model is shown to satisfy important requirements such as providing a unique solution and being anisotropic. Simulations are applied to compare Fastlane to other multiclass models. Furthermore, we show that the characteristic velocity depends on the truck share, which is one of the main consequences of our modeling approach.
    Transportation Research Record Journal of the Transportation Research Board 01/2014; DOI:10.3141/2422-06 · 0.44 Impact Factor
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    ABSTRACT: In this article we demonstrate how network components can be modeled using the kinematic wave model in the Lagrangian formulation. This includes modeling nodes (or discontinuities) such as inflow and outflow boundaries, merges and bifurcations (e.g. ramps) and nonhomogeneous roads. Nodes are usually fixed in space. This makes their implementation in Lagrangian coordinates where the coordinates move with the vehicle more complex than in Eulerian coordinates where the coordinates are fixed in space. To this end we derive an analytical node model. The article then discusses how to implement such sink and source terms in a discretized version of the kinematic wave model in Lagrangian coordinates. In this implementation several choices have to be made. Test results show that even with the most simple choices (discretization based on full vehicle groups and discrete time steps) accurate and plausible results are obtained. We conclude that the Lagrangian formulation can successfully be applied for simulation of networks of nonhomogeneous roads. {\copyright} 2011 Elsevier Ltd. All rights reserved.
    Transportation Research Part C Emerging Technologies 09/2013; 34:148–161. DOI:10.1016/j.trc.2011.08.004 · 2.01 Impact Factor
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    ABSTRACT: This report gives an overview of the development and experiences of using Mumie [1] at TU Delft during the academic year 2010-2011. Mumie is an e-learning platform that can be used for mathematical courses and acquired the interest of TU Delft at the beginning of 2009 in order to be used in their first years mathematical courses, in particular Linear Algebra . To see if Mumie could be successfully used at TU Delft, a pilot experiment was held under Aerospace Engineering students for a small part of the LA course. The outcome of this pilot was good, around 70% of the students recommended to use Mumie for the course, so further development of Mumie at TU Delft continued and is discussed in this report. Earlier reports on the development of Mumie at TU Delft can be found at the Mumie wiki [2]. Section 2 gives an update on the progress that has been made since the pilot. In Section 3 there is an overview of the student survey and grades for 2010/2011. Finally, in Section 4 conclusions are drawn from the survey results and student grades, together with a discussion and points of improvement for the future. Throughout this report some terms will be used that you might not be familiar with: AE the study Aerospace Engineering at TU Delft LA the Linear Algebra course at TU Delft CS the Computer Science course at TU Delft VWO this is highest level in the Dutch high school system
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    ABSTRACT: In this document the Mumie pilot that took place in March 2010 for the Linear Algebra course (wi1403lr) at Aerospace Engineering will be evaluated. This pilot is the result of an interest in using an e-learning platform that can improve the level of education for first year mathematical courses at TU Delft. In order to be successful with such projects it is important that the end-users, students and teachers in this case, are willing to accept using it. With no support from this group it is very difficult to introduce such a project successfully. To get an idea of the opinion of the endusers, the pilot has been organised. What can one expect to find in this document? At first, an overview of the current method of teaching for the Linear Algebra course will be presented together with the different phases that took place prior to the pilot. Chapter 3 will take a look at the set-up of the pilot, followed by an analysis of the feedback given by the students on the pilot in Chapter 4. In the last two chapters the conclusions and recommendations from the pilot will be presented, Chapter 5, together with the future plans and improvements in Chapter 6. This document won’t go into the details of Mumie, for more information on this visit www.mumie.net, also there is a wiki for the use at TU Delft, see https://www.mumie.net/wiki(note: it is https instead of http) and click on the TU Delft section. The pilot has been set up by the following people. Coordination is in hands of Kees Vuik, Fons Daalderop is the teacher, Robert van Kints and Bart Schaap are responsible for the implementation of the pilot. Furthermore usefull feedback and ideas have been given by Paul Visser. Wim Caspers helps us to have an idea what is going on at the TU Delft with respect to e-learning.
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    ABSTRACT: Traffic flow models and simulation tools are often used for traffic state estimation and prediction. Recently several multi-class models based on the kinematic wave traffic flow model have been introduced. These multi-class models take into account the heterogeneity of both vehicles and drivers. We analyse two important properties of these models: hyperbolicity and anisotropy. Both properties relate to the propagation speed of disturbances, as can be observed in real traffic. We discuss the importance of traffic flow models to be hyperbolic and anisotropic. Moreover, we develop a framework to analyse whether traffic flow models have these properties. Therefore, we derive a generic formulation of multi-class kinematic wave traffic flow models, rewrite it in the Lagrangian formulation and apply eigenvalue analysis to the resulting system of equations. Our analysis shows that most multi-class kinematic wave traffic flow models are indeed hyperbolic and anisotropic under certain modelling conditions.
    Transportmetrica 01/2011; 9(5):1-22. DOI:10.1080/18128602.2011.596289 · 1.36 Impact Factor
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    Conference Paper: Fast Newton load flow
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    ABSTRACT: The Newton-Raphson method is widely used to solve load flow problems. Traditionally a direct solver is used to solve the linear systems within this method. In this paper we explore the use of an iterative method to solve the linear systems, leading to an inexact Newton-Krylov method. The main parameters of this method are the preconditioner and the forcing terms. Several candidate choices for these parameters are discussed and tested. With the proper preconditioner, and forcing terms, the inexact Newton-Krylov method is shown to greatly improve on using a direct solver.
    Transmission and Distribution Conference and Exposition, 2010 IEEE PES; 05/2010
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    ABSTRACT: The present paper consists of the formulation of a model for particle dissolution in a multi-component alloy taking into account cross-diffusion effects. The model consists of a Stefan condition to compute the velocity of the interface separating the particle and the solvent phase. The influence of the cross-diffusion terms on the particle dissolution rate is shown and it is concluded that its impact can be significant.
    Solid State Transformation and Heat Treatment, 08/2005: pages 53 - 60; , ISBN: 9783527604838
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    ABSTRACT: Large linear systems are solved for modeling many scientific and engineering applications. Often these systems result from a discretization of model equations using Finite Elements, Finite Volumes or Finite Differences. The systems tend to become very large for three dimensional problems. Some models involve both time and space as independent parameters and therefore it is necessary to solve such a linear system efficiently at all time-steps.
    12/2003: pages 103-129;
  • Kees Vuik
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    Fred Vermolen, Kees Vuik
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    ABSTRACT: Dissolution of stoichiometric multi-component particles in ternary alloys is an important process occurring during the heat treatment of as-cast aluminium alloys prior to hotextrusion. A mathematical model is proposed to describe such a process. In this model an equation is given to determine the position of the particle interface in time, using two diffusion equations which are coupled by nonlinear boundary conditions at the interface. Some results concerning existence, uniqueness, and monotonicity are given. Furthermore, for an unbounded domain an analytical approximation is derived. The main part of this work is the development of a numerical solution method. Finite differences are used on a grid which changes in time. The discretization of the boundary conditions is important to obtain an accurate solution. The resulting nonlinear algebraic system is solved by the Newton-Raphson method. Numerical experiments illustrate the accuracy of the numerical method. The numerical solution is compared with the analytical approximation. Keywords: Stefan problem, moving grid method, stoichiometric particle dissolution, ternary alloy homogenisation AMS Subject Classification: 35R35, 65M06, 80A22 1
    Journal of Computational and Applied Mathematics 09/2001; DOI:10.1016/S0377-0427(98)00076-4 · 1.08 Impact Factor
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    Guus Segal, Kees Vuik
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    ABSTRACT: In this paper we consider the solution of the systems of non-linear equations
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    ABSTRACT: For the solution of practical complex problems in arbitrarily shaped domains, simple
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    ABSTRACT: For the solution of practical flow problems in arbitrarily shaped domains, simple Schwarz
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    ABSTRACT: In a previous article [1], the eigenvalues of the elasto-plastic material matrix of a Drucker-Prager nonassociated soil model were analyzed with special attention to the occurrence of complex eigenvalues. The link between this analysis on material level to stress states which arise in a numerical computation is made in this article. © 1999 Elsevier Science Ltd. All rights reserved.
    Computers & Mathematics with Applications 11/1999; 38(s 9–10):245–249. DOI:10.1016/S0898-1221(99)00279-5 · 2.00 Impact Factor
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    ABSTRACT: The transition from homogeneous to localized deformation during the loading of a soil specimen within a finite element computation is frequently characterized by a bifurcation point, indicating loss of uniqueness of the solution. Often, the signaling of bifurcation is done via the eigenvalues of structural matrix resulting from finite element discretization. Eigenvectors related to negative eigenvalues can be used to perturb an unstable state and to arrive at a stable path. This procedure is called branch switching and is briefly reviewed. The signaling of bifurcation is reconsidered with respect to nonsymmetry and positive definiteness of the structural matrix, and is related to loss of stability.
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    ABSTRACT: Theory An iterative numerical method for solving the wave equation in an inhomogeneous medium with constant density is presented. The method is based on a Krylov iterative method and enhanced by a powerful preconditioner. For the preconditioner, a complex Shifted- Laplace operator is proposed, designed specifically for the wave equation. A multigrid method is used to approximately compute the inverse of the preconditioner. Numerical examples on 2D problems show that the combined method is robust and applicable for a wide range of frequencies. Extension to 3D is straightforward. The time-harmonic wave problem is represented by the Helmholtz equation:
    SEG Technical Program Expanded Abstracts 01/1999; 23(1). DOI:10.1190/1.1845184
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    ABSTRACT: A numerical analysis of the homogenisation treatment of aluminium alloys under industrial circumstances is presented. The basis of this study is a mathematical model which is applicable to the dissolution of stoichiometric multicomponent phases in both finite and infinite ternary media. It handles both complete and incomplete particle dissolution as well as the subsequent homogenisation of the matrix. The precipitate volume fraction and matrix homogeneity are followed during the entire homogenisation treatment. First, the influence of the metallurgical parameters, such as particle size distribution, initial matrix concentration profile and particle geometry on the dissolution- and matrix homogeneity kinetics is analysed. Then, the impact of the heating-rate and local temperature on the homogenisation kinetics is investigated. Conclusions for an optimal homogenisation treatment of aluminium alloys may be drawn. The model presented is general but the calculations were performed for the system Al–Mg–Si with an Al-rich matrix and Mg2Si-precipitates.
    Materials Science and Engineering A 10/1998; 254(1-2-254):13-32. DOI:10.1016/S0921-5093(98)00763-1 · 2.41 Impact Factor
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    ABSTRACT: The transition from homogeneous to localized deformations during the loading of a soil specimen within a ®nite element com-putation is often characterized by a bifurcation point, indicating loss of uniqueness of the solution. The signalling of a bifurcation point is done via the eigenvalues of the structural sti€ness matrix resulting from the ®nite element discretization. Eigenvectors related to negative eigenvalues can be used to perturb a homogeneous state and to obtain a localized deformation mode. This procedure is called branch switching. Several methods are proposed to perform this branch switching.
    Computer Methods in Applied Mechanics and Engineering 07/1998; 190(5). DOI:10.1016/S0045-7825(99)00439-9 · 2.63 Impact Factor