Two-phase SPH modelling of advective diffusion processes

This paper deals with a two-dimensional numerical model based on the smoothed particle hydrodynamics (SPH) technique for the evaluation of the concentration field of pollutants in water. A SPH model is formulated to solve the fickian diffusion equation applied to pollutants with the same density as the water. A lagrangian SPH formalism of the advective diffusion equation is also developed for pollutant-water, taking into account the effects of molecular diffusion and natural advection induced by differences between the fluid densities. These equations are coupled with the fluid mechanics equations. Attention is paid to the numerical aspects involved in the solution procedure and to the optimization of the model parameters. Environmental engineering problems concerning diffusion and natural advection phenomena occur in the presence of a pollutant in still water. Numerical tests referring to a strip and a bubble of contaminant in a water tank with different initial concentration laws have been carried out. The results obtained by the proposed SPH models are compared with other available SPH formulations, showing an overall better agreement with standard analytical solutions in terms of spatial evolution of the concentration values. Capabilities and limits of the proposed SPH models to simulate advective diffusion phenomena for a wide range of density ratios are discussed.