Discrete Particle Distribution Model for Advection-Diffusion Transport

A new methodology, named DisPar, based on a discrete probability distribution for a particle displacement, was developed to solve 1D advection-diffusion transport problems in water bodies. The discrete probability distribution for the particle displacement was developed as an average and variance function. These probabilities were used to predict the deterministic mass transfer between cells in one time step, and therefore the particle concentration in each cell was considered the state variable. The state equation was found to be similar to an explicit finite-difference formulation with a Eulerian grid. The model stability, positivity, and mass conservation are guaranteed by the probability distribution concept. DisPar produces solutions without numerical dispersion for constant velocity, diffusion coefficient, and cross-sectional area. In these conditions, DisPar was also developed as a function of space and time for an instantaneous mass spill. When the stability and positivity restrictions were respected, the model produced excellent results when compared to analytical solutions and other methods. The discrete particle displacement distribution concept differs from other numerical formulations, and therefore it represents a new modeling technique.