Numerical Methods and Tangible Interfaces for run.unl.pt/bitstream/10362/9305/1/Ferreira_2005.pdf ·…

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  • Joo Serpa Soares Moradas Ferreira

    Numerical Methods and Tangible Interfaces for

    Pollutant Dispersion Simulation

    Dissertao apresentada para obteno do Grau de Doutor em Engenharia do

    Ambiente, pela Universidade Nova de Lisboa, Faculdade de Cincias e Tecnologia

    Lisboa, 2005

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    To my son Andr

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    Acknowledgements

    Many people have helped me and contributed to this thesis:

    Prof. Antnio Cmara, my research advisor, for having accepted me as a Phd student and for

    his constant motivation to work on the frontiers of new ideas;

    Manuel Costa, who is co-author of DisPar methods, has given an indispensable contribution to

    the work presented in this thesis;

    YDreams team that worked with me on TangiTable concept and implementation: Edmundo

    Nobre, for sharing with me the idea of a tangible interface for pollutant dispersion simulation; Ivan

    Franco, who oriented its physical implementation in the Engenho e Obra exhibition; Nuno Cardoso,

    for the implementation of the computer vision algorithms; Antnio Lobo and Pedro Lopes for the

    graphic design. I also thank all other people involved in this project;

    Cristina Gouveia e Jos Carlos Danado, for their many suggestions on general topics, such as

    public participation and augmented reality;

    Andr Fortunato and Anabela Oliveira, for their support in transport modelling theory, and also

    for making available the hydrodynamic data of the Tagus Estuary;

    Prof. Carmona Rodrigues, for having taught me the fundamentals of numerical methods and for

    encouraging me to have new ideas in this research field;

    Conceio Capelo and Telma Loureno, for their assistance in administrative work;

    Finally and very especially, I thank all my family and friends, for everything.

    This work was supported by Fundao para a Cincia e Tecnologia (FCT) from the Portuguese

    Ministry of Science and Technology under the scholarship contract BD/5064/2001 and the research

    contract MGS/33998/99-00.

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    Abstract

    The first main objective of this thesis is to reduce numerical errors in advection-diffusion

    modelling. This is accomplished by presenting DisPar methods, a class of numerical schemes for

    advection-diffusion or transport problems, based on a particle displacement distribution for Markov

    processes. The development and analyses of explicit and implicit DisPar formulations applied to one

    and two dimensional uniform grids are presented. The first explicit method, called DisPar-1, is based

    on the development of a discrete probability distribution for a particle displacement, whose numerical

    values are evaluated by analysing average and variance. These two statistical parameters depend on

    the physical conditions (velocity, dispersion coefficients and flows). The second explicit method,

    DisPar-k, is an extension of the previous one and it is developed for one and two dimensions. Besides

    average and variance, this method is also based on a specific number of particle displacement

    moments. These moments are obtained by the relation between the advection-diffusion and the

    Fokker-Planck equation, assuming a Gaussian distribution for the particle displacement distribution.

    The number of particle displacement moments directly affects the spatial accuracy of the method, and

    it is possible to achieve good results for pure-advection situations. The comparison with other methods

    showed that the main DisPar disadvantage is the presence of oscillations in the vicinity of step

    concentration profiles. However, the models that avoid those oscillations generally require complex

    and expensive computational techniques, and do not perform so well as DisPar in Gaussian plume

    transport. The application of the 2-D DisPar to the Tagus estuary demonstrates the model capacity of

    representing mass transport under complex flows. Finally, an implicit version of DisPar is also

    developed and tested in linear conditions, and similar results were obtained in terms of truncation error

    and particle transport methods.

    The second main objective of this thesis, to contribute to modelling cost reduction, is

    accomplished by presenting TangiTable, a tangible interface for pollutant dispersion simulation

    composed by a personal computer, a camera, a video projector and a table. In this system, a virtual

    environment is projected on the table, where the users place objects representing infrastructures that

    affect the water of an existent river and the air quality. The environment and the pollution dispersion

    along the river are then projected on the table. TangiTable usability was tested in a public exhibition

    and the feedback was very positive. Future uses include public participation and collaborative work

    applications.

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    Sumrio

    O primeiro objectivo da presente dissertao corresponde reduo de erros numricos em

    formulaes de adveco-difuso e efectuado atravs da apresentao dos mtodos DisPar. Estes

    mtodos so uma classe de formulaes numricas de adveco-difuso, baseada em distribuies

    do deslocamento de partculas para processos de Markov. Esto includos os desenvolvimentos,

    anlises formais e testes de mtodos DisPar explcitos e implcitos aplicados em malhas uniformes

    uni-dimensionais e bi-dimensionais. O primeiro mtodo, DisPar-1, baseado no desenvolvimento da

    distribuio de probabilidade discreta do movimento de uma partcula, cujos valores so inferidos a

    partir da mdia e varincia do deslocamento. Estes dois parmetros estatsticos dependem das

    condies fsicas (velocidade, coeficientes de disperso e fluxos). O Segundo mtodo explcito,

    DisPar-k, desenvolvido para uma e duas dimenses, uma extenso do anterior. Para alm da mdia

    e da varincia, a distribuio do deslocamento de uma partcula baseia-se num nmero especfico de

    momentos. Os momentos so obtidos atravs da relao entre as equaes de adveco-difuso e

    Fokker-Planck, assumindo uma distribuio de Gauss para o movimento das partculas. O nmero de

    momentos afecta de uma forma directamente proporcional a preciso espacial do mtodo, sendo

    possvel obter bons resultados em situaes de adveco pura. Nestas situaes, a comparao com

    outros mtodos demonstrou que a principal desvantagem do DisPar, em 1-D e 2-D, a presena de

    oscilaes nas vizinhanas de perfis de concentrao descontnuos. No entanto, os mtodos que

    evitam estas oscilaes, apresentam piores resultados que o DisPar-k no transporte de perfis mais

    alisados. A aplicao do DisPar 2-D ao esturio do Tejo demonstrou a capacidade do mtodo de

    representar o transporte de massa em escoamentos complexos. Finalmente, uma verso 1-D

    implcita do DisPar igualmente apresentada, obtendo-se uma relao semelhante entre os erros de

    truncatura e os momentos de deslocamento das partculas.

    O contributo para a reduo do custo de modelao, segundo objectivo de dissertao, obtido

    atravs da apresentao da TangiTable, uma interface tangvel para a simulao da disperso de

    poluentes, composta por uma computador pessoal, uma cmara, um projector de video e uma mesa.

    Neste sistema, um ambiente virtual projectado sobre uma mesa, na qual utilizadores colocam

    objectos representando infra-estruturas que afectam a gua de um rio e a qualidade do ar. O

    ambiente e a disperso da poluio so dinamicamente projectados na mesa. A usabilidade da

    TangiTable testada com resultados bastante positivos numa exposio aberta ao pblico e usos

    potenciais incluem participao pblica e trabalho colaborativo.

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    Notation

    Chapter 2

    xa - x expectation of order a;

    A section area;

    B(x,t) - tensor that characterizes the random forces;

    C concentration;

    D dispersion or Fickian coefficient;

    P(x,t) probability for a particle to be in x at time t;

    P(xn,tn|x1,t1;;xn-1,tn-1) - transition probability of a particle to be in position xn at time tn if it was in position x1,...xn-1 at time t1,....tn-1, respectively;

    P(xn,tn|xn-1,tn-1) probability for a particle to be in xn at time tn if it was in xn-1 at time t1;

    t time;

    W(x,t) - vector representing the deterministic forces that act to change x(t);

    x space;

    (t) - vector composed of random numbers that represent the chaotic nature of turbulent particle motion;

    Chapter 3

    Ai - cell i section area;

    B - random forces tensor;

    C.n - cell i concentration in time n;

    C(x,t) - concentration field;

    D0 - constant diffusion coefficient;

    Di - cell i Fickian coefficient;

    ds_dispid - downstream average dispersion velocity;

    us_dispid - upstream average dispersion velocity;

    adv

    ix - particle advective displacement average;

    disp

    ix - particle dispersive displacement average;

    tot

    ix - particle displacement total average;

    tot

    idx - particle displacement total average measured in distance;

    f - particle probability density function;

    i - discrete space index;

    niM - cell i particle mass in time n;

    n - discrete time index ;

    P(x,n+1|i,n) - probability that a particle will move from node i to node x over a time step;

    Padv(x,n+1|i,n) - probability that a particle will move from node i to node x over a time step due to advection;

    Pdisp(x,n+1|i,n) - probability that a particle wi