| Contents |
| In this paper we will present the main problems environmental dispersion in the region of Mato Grosso, strategies for Mathematical modelling for the problems and methods of
numerical approximation of the solution. As an illustration, we will be present some computer simulations of problems already studied and the prospects for future work.
In general, the equation that models the phenomenon dispersion, known transport equation, generally, can be modeled by:
$$\left\{\begin{array}{c} \textrm{ the variation of}\\
\textrm{ pollutant concentration} \end{array}
\right\} =
\left\{\begin{array}{c} \textrm{diffusion}\\
\textrm{process}
\end{array} \right\} - \left\{\begin{array}{c} \textrm{transport}\\
\textrm{by the environment} \end{array} \right\} -
\left\{\begin{array}{c} \textrm{degradation}\\
\textrm{by the environment} \end{array} \right\} +
\left\{\begin{array}{c} \textrm{source}\\
\textrm{term} \end{array} \right\}
$$
where each of the terms listed above has been treated in literature by several authors.
For simulations of scenarios, one gets the variational formulation the proposed by PDE classic model, whose discretizations in the space and time, has been made by the finite elements method (for spatial discretization), by Petrov/Galerkin scheme and Crank-Nicolson (for temporal discretization), for numerical approximation of the solutions.
The program MATLAB$^R$ has proven more efficient for implementation of numerical codes providing the graphic animations that will be shown.
Keywords: Diffusion-reaction equation, environmental impacts and pollutant transport |
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