Given a numerical model for solving two-dimensional shallow water equations, we are interested in the robustness of the simulation by identifying the rate of change of the water depths and discharges with respect to a change in the bottom friction coefficients. Such a sensitivity analysis can be carried out by computing the corresponding derivatives. Automatic differentiation (AD) is an efficient numerical method, free of approximation errors, to evaluate derivatives of the objective function specified by the computer program, Rubar20 for example. In this paper AD software tool Tapenade is used to compute forward derivatives. Numerical tests were done to show the robustness of the model and to demonstrate the efficiency of these AD-derivatives.

No abstract

No abstract

The modeling of atmospheric dispersion is the mathematical simulation of how pollutants are dispersed in the atmosphere. Based on the advection-diffusion equations describing the dispersion of pollutants, dispersal models are widely used to give a spatial variability of pollutants emitted mainly by agricultural activities and industrial facilities. In this context, an analytical model is presented to study the dispersion of pollutants in the atmospheric boundary layer. The solution procedure is based on dividing the planetary boundary layer into sub-domains, where in each sub-domain the eddy diffusivity and the wind speed take average values. The eddy diffusivity is expressed under unstable conditions and the wind speed is represented in its logarithmic form. The findings of the current study show that the developed model is successfully validated using data sets obtained from the Copenhagen diffusion experiments in unstable conditions, after this the model is numerically applied in order to observe, in a better way, the spread of the pollutant in the atmosphere.

No abstract