Computation of dye concentration in shallow recirculating flow

The Lagrangian second-moment method is used to compute the dye-concentration distribution in turbulent recirculating flow generated in a shallow open channel by a sudden widening of how in the transverse direction. The performance of the second-moment method is compared with the Eulerian numerical schemes of Upwind, QUICK, HLPA, and the semi-Lagrangian Hermite scheme. The results show that the Lagrangian second-moment method is an accurate and a very promising scheme for the computation of concentration distribution in flows dominated by advection. It minimizes the generation of numerical diffusion, is free from numerical oscillations, and is independent of the value of Courant number. Its efficiency in terms of computational time is high in flows where the mixing is confined to a small region of the solution domain and low in hows where the mixing is extended in the whole solution domain. In addition to an accurate numerical scheme, a necessary requirement for the accurate prediction of concentration field is a hydrodynamic model able to determine correctly the velocity held and the diffusion coefficient in shallow recirculating flows.