Journal : Acta Geophysica
Article : The numerical solution of the Advection-Dispersion Equation: A review of some basic principles

Authors :
Rowiński, P.
Institute of Geophysics, Polish Academy of Sciences, Księcia Janusza 64, 01-452 Warszawa, Poland,,
Nikora, V.
Engineering Department, University of Aberdeen, King’s College, Scotland, UK,,
Majewski, W.
Institute of Meteorology and Water Management, ul. Podleśna 61, 01-673 Warszawa, Poland,,
Aberle, J.
Leichtweiss-Institute for Hydraulic Engineering, Technical University of Braunschweig, Beethovenstr. 51, 38106 Braunschweig, Germany,,
Dittrich, A.
Leichtweiss-Institut of Hydraulic Engineering (LWI), Department of Hydraulic Engineering, Beethovenstrasse 51a, 38106 Braunschweig, Germany,,
Brovchenko, I.
Ukrainian Center of Environmental and Water Projects Glushkova Prospect 42, 03187, Kiev, Ukraine,,
Demchenko, N.
Atlantic Branch of P.P. Shirshov Institute of Oceanology Russian Academy of Sciences Prospect Mira 1, 236000 Kaliningrad, Russia,,
Néelz, S.
Heriot-Watt University, Riccarton, Edinburgh, EH14 4AS, UK,,
Wörman, A.
Environmental Physics Group, Swedish University of Agricultural Sciences, Uppsala, Sweden,,
Wallis, S.
Heriot-Watt University, Riccarton, Edinburgh, EH14 4AS, UK, s.g.wallis@,
Abstract : The simulation of solute transport in rivers is frequently based on numerical models of the Advection-Dispersion Equation. The construction of reliable computational schemes, however, is not necessarily easy. The paper reviews some of the most important issues in this regard, taking the finite volume method as the basis of the simulation, and compares the performance of several types of scheme for a simple case of the transport of a patch of solute along a uniform river. The results illustrate some typical (and well known) deficiencies of explicit schemes and compare the contrasting performance of implicit and semi-Lagrangian versions of the same schemes. It is concluded that the latter have several benefits over the other types of scheme.

Keywords : solute transport, numerical modelling, finite volume method, advection, reference frame, time marching,
Publishing house : Instytut Geofizyki PAN
Publication date : 2007
Number : Vol. 55, no. 1
Page : 85 – 94

: Leonard, B.P., 1979, A stable and accurate convective modeling procedure based on quadratic upstream interpolation, Computer Meth. Appl. Mech. Eng. 19, 59-98.
Rutherford, J.C., 1994, River Mixing, J. Wiley and Sons Ltd., New York, 347 pp.
Versteeg, H.K., and W. Malalasekera, 1995, An Introduction to Computational Fluid Dynamics: The Finite Volume Method, Addison-Wesley Longman Ltd., UK, 257 pp.
Wallis, S.G., and J.R. Manson, 1997, Accurate numerical simulation of advection using large time steps, Int. J. Numer. Meth. Fluids 24, 127-39.
Wallis, S.G., J.R. Manson and L. Filippi, 1998, A conservative semi-Lagrangian algorithm for one-dimensional advection-diffusion, Comm. Numer. Meth. Eng. 14, 671-679.
Qute : Rowiński, P. ,Nikora, V. ,Majewski, W. ,Aberle, J. ,Dittrich, A. ,Brovchenko, I. ,Demchenko, N. ,Néelz, S. ,Wörman, A. ,Wallis, S. ,Wallis, S. , The numerical solution of the Advection-Dispersion Equation: A review of some basic principles. Acta Geophysica Vol. 55, no. 1/2007