An explicit algorithm to simulate transient transverse mixing in rivers

Abstract

Because no analytical solution exists for transient mixing of contaminants in the transverse mixing zone of streams, numerical solutions must be used in pertinent engineering applications. Few numerical algorithms have been devehloped for this problem and the relatively simple explicit ones are subject to serious numerical "diffusion." It is suggested herein that such effects can be minimized using an irregular space grid such that the length of each element is exactly equal to the time step times the local flow velocity. Using also the well-known streamtube concept, a simple explicit algorithm is obtained and verified by means of three laboratory and one field test. Two of these tests include concentration data that are both transient and within the transverse mixing zone, which afford a more complete algorithm testing than has been done in the past. Possible improvements for increased accuracy, efficiency, and generalized natural stream application are discussed. Key words: advection, algorithm, channel, diffusion, dispersion, explicit, mixing, numerical, numerical diffusion, river, streamtube, test, transient, transverse.