SEMI-IMPLICIT ADVECTION DIFFUSION PARTICLE DISTRIBUTION MODEL

摘要

In this paper, a semi-implicit version of the DisPar model, applied to uniform grids, is presented and tested. The DisPar model solves advection-diffusion problems based on a particle displacement probability for Markov processes. The formulation is developed by establishing a relation between the particle displacement average and variance and the model state equation coefficients. An explicit mass transfer is incorporated in the model to avoid Courant number restrictions. The model formal analysis shown that the model converges to the transport equation. A minimal dispersion coefficient value guarantees stability and positivity in the solutions. In linear conditions Semi-implicit DisPar do not present numerical dispersion and a relation it is presented a relation between particle statistical parameters and numerical errors. The model is a good alternative in diffusivity-dominated situations and future developments can improve the model performance in advection-dominated situations, following the same principles from explicit DisPar versions.