Adaptive particle method based on moments for simulating the mass transport in natural flows

Abstract

In this work, two modifications of an adaptive particle method based on the moments of the internal concentration of numerical particles are presented to introduce the effect of local shears on the mass transport in natural flows. This moment method uses a Taylor expansion of the flow velocity field to derive the transport equation of moments. The first modification is based on the introduction of a method of the local frame transport in order to perform an extension of the Taylor expansion of the flow velocity to a higher order. The second modification consists in applying a splitting or a merging to non-spherical numerical particles. When a non-spherical numerical particle becomes large compared to the scale of spatial variations of the velocity gradient, it is divided into two non-spherical numerical particles. On the contrary, when particles reach some other parts of the flow where they become small compared to spatial variations of the velocity gradient, then these particles should merge. The accuracy of both modifications is evaluated by simulating the mass transport in natural flows.