Tracking accuracy of a semi-Lagrangian method for advection-dispersion modelling in rivers

There is an increasing need to improve the computational efficiency of river water quality models because: (1) Monte-Carlo-type multi-simulation methods, that return solutions with statistical distributions or confidence intervals, are becoming the norm, and (2) the systems modelled are increasingly large and complex. So far, most models are based on Eulerian numerical schemes for advection, but these do not meet the requirement of efficiency, being restricted to Courant numbers below unity. The alternative of using semi-Lagrangian methods, consisting of modelling advection by the method of characteristics, is free from any inherent Courant number restriction. However, it is subject to errors of tracking that result in potential phase errors in the solutions. The aim of this article is primarily to understand and estimate these tracking errors, assuming the use of a cell-based backward method of characteristics, and considering conditions that would prevail in practical applications in rivers. This is achieved separately for non-uniform flows and unsteady flows, either via theoretical considerations or using numerical experiments. The main conclusion is that, tracking errors are expected to be negligible in practical applications in both unsteady flows and non-uniform flows. Also, a very significant computational time saving compared to Eulerian schemes is achievable. Copyright © 2006 John Wiley & Sons, Ltd.