Numerical Methods and Tangible Interfaces for Pollutant Dispersion Simulation

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.