Lagrangian modeling of advection‐diffusion transport in open channel flow

Abstract

A fully Lagrangian method is presented for the accurate simulation of advection‐diffusion transport in both steady and unsteady open channel flows. Numerical results are presented for Gaussian tracer distributions, top hat tracer distributions, and steep tracer fronts (step function) profiles in a uniform flow and are compared against analytical solutions and against the results obtained with an Eulerian Quadratic Upstream Interpolation for Convective Kinematics with Estimated Streaming Terms (QUICKEST) method. It is demonstrated that the Lagrangian scheme can totally eliminate numerical diffusion and oscillations including those normally observed in steep frontal regions in most Eulerian schemes. In steady, uniform flow, the scheme allowed a large time step to be used and provides exact solutions for a wide range of Courant numbers (results are presented for Cr from 0 to 20) and for an entire range of grid Peclet numbers (from 0 to infinity). These simulation results for a uniform flow were extended to flows due to simple waves, solitary waves, and undular bores; again, the scheme produced excellent results. It is shown that the simple Lagrangian model is an efficient and accurate tool to predict transport in advection dominated systems, and when it is coupled with the new Lagrangian river model, the dynamic river model, it can be an ideal model for long‐term and large‐scale simulation of transport for water quality in river systems and for transport with steep frontal regions.