Divergence-free condition in transport simulation

In this work, two adaptations of the particle method allowing one to reduce the numerical errors induced by the non-zero divergence of flow fields in the numerical simulations of particle transport are presented. The first adaptation is based on the renormalization method allowing one to use an irregular distribution of particles induced by the non-zero divergence of flow fields. The second adaptation consists in applying a correction on the weight of the particles by using the relation between the divergence of flow fields and the particles' volume evolution. This adaptation may be considered as a relaxation method. The accuracy of both methods is evaluated by simulating the transport of an inert tracer by the flow of a jet in crossflow whose concentration fields were measured experimentally. The comparison between the numerical and experimental results shows clearly that the two adaptations of the particle method correct efficiently the effect of a non-zero divergence velocity field on the computed concentration.