Pollutant Dispersion Modeling in Natural Streams Using the Transmission Line Matrix Method

Numerical modeling has become an indispensable tool for solving various physical problems. In this context, we present a model of pollutant dispersion in natural streams for the far field case where dispersion is considered longitudinal and one-dimensional in the flow direction. The Transmission Line Matrix (TLM), which has earned a reputation as powerful and efficient numerical method, is used. The presented one-dimensional TLM model requires a minimum input data and provides a significant gain in computing time. To validate our model, the results are compared with observations and experimental data from the river Severn (UK). The results show a good agreement with experimental data. The model can be used to predict the spatiotemporal evolution of a pollutant in natural streams for effective and rapid decision-making in a case of emergency, such as accidental discharges in a stream with a dynamic similar to that of the river Severn (UK).

[1]  S. Chapra.  Surface Water-Quality Modeling , 1996 .

[2]  Daniel Sztruhar,et al.  Enhancing urban environment by environmental upgrading and restoration , 2005 .

[3]  Il Won Seo,et al.  Routing procedures for observed dispersion coefficients in two-dimensional river mixing , 2010 .

[4]  T. Day,et al.  Longitudinal dispersion in natural channels , 1975 .

[5]  L. Ridolfi,et al.  Longitudinal dispersion in vegetated rivers with stochastic flows , 2010 .

[6]  Gwenaël Guillaume.  Application de la methode TLM a la modelisation de la propagation acoustique en milieu urbain , 2009 .

[7]  R. Runkel,et al.  One-Dimensional Transport with Inflow and Storage (OTIS): A Solute Transport Model for Small Streams , 1991 .

[8]  Evaluation of dispersion parameters for River São Pedro, Brazil, by the simulated annealing method , 2013 .

[9]  R. Courant,et al.  On the Partial Difference Equations, of Mathematical Physics , 2015 .

[10]  I Guymer,et al.  Longitudinal mixing in meandering channels: new experimental data set and verification of a predictive technique. , 2007, Water research.

[11]  C. Keylock,et al.  The application of computational fluid dynamics to natural river channels: Eddy resolving versus mean flow approaches , 2012 .

[12]  Tim Atkinson,et al.  Longitudinal dispersion in natural channels: l. Experimental results from the River Severn, U.K. , 2000 .

[13]  Ayda Saïdane,et al.  Thermal analysis of a three-dimensional breast model with embedded tumour using the transmission line matrix (TLM) method , 2011, Comput. Biol. Medicine.

[14]  H. Fischer,et al.  Longitudinal dispersion in laboratory and natural streams , 1966 .

[15]  M. Y. Al-Zeben,et al.  TLM modelling of diffusion, drift and recombination of charge carriers in semiconductors , 1992 .

[16]  P. B. Johns.  On the Relationship Between TLM and Finite-Difference Methods for Maxwell's Equations (Short Paper) , 1987 .

[17]  Kenneth M Persson,et al.  Sinuosity effects on Longitudinal Dispersion Coefficient , 2010 .

[18]  E. Anderson,et al.  Estimating longitudinal dispersion in rivers using Acoustic Doppler Current Profilers , 2010 .

[19]  C. Christopoulos,et al.  The Transmission-line Modeling Method: TLM , 1995, IEEE Antennas and Propagation Magazine.

[20]  Morten Nielsen,et al.  An evaluation of validation procedures and test parameters for dense gas dispersion models , 1996 .

[21]  Roger A Falconer,et al.  Longitudinal dispersion coefficients in natural channels. , 2002, Water research.

[22]  Amir Etemad-Shahidi,et al.  Predicting Longitudinal Dispersion Coefficient in Natural Streams Using M5′ Model Tree , 2012 .

[23]  Hazi Mohammad Azamathulla,et al.  Genetic Programming for Predicting Longitudinal Dispersion Coefficients in Streams , 2011 .

[24]  Adam P. Piotrowski,et al.  Comparison of evolutionary computation techniques for noise injected neural network training to estimate longitudinal dispersion coefficients in rivers , 2012, Expert Syst. Appl..

[25]  W. Graf.  Fluvial Hydraulics: Flow and Transport Processes in Channels of Simple Geometry , 1998 .

[26]  Sandrick Le Maguer.  Developpements de nouvelles procedures numeriques pour la modelisation tlm : application a la caracterisation de circuits plaques et de structures a symetrie de revolution en bande millimetrique , 1998 .

[27]  Donard De Cogan.  Transmission line matrix (TLM) techniques for diffusion applications , 1998 .

[28]  L. Ridolfi,et al.  Estimation of the dispersion coefficient in rivers with riparian vegetation , 2009 .

[29]  Daas Jabbour.  Etude expérimentale et modélisation de la dispersion en champ lointain suite à un rejet accidentel d'un polluant miscible dans un cours d'eau. Application à la gestion de crise. , 2007 .

[30]  Mohamed Henini,et al.  Transmission-line matrix (TLM): a novel technique for modelling reaction kinetics , 1987 .

[31]  Electromagnetic transient scattering analysis in time-domain—comparison of TLM and TDIE methods , 2012 .

[32]  Dong Chen,et al.  Evaluating secondary flows in the evolution of sine-generated meanders , 2012 .

[33]  H. Fischer.  Mixing in Inland and Coastal Waters , 1979 .

[35]  Pius Lee,et al.  Evaluation of the Operational Multiscale Environment Model with Grid Adaptivity against the European Tracer Experiment , 2001 .

[36]  Dongsu Kim.  Assessment of longitudinal dispersion coefficients using Acoustic Doppler Current Profilers in large river , 2012 .

[37]  Juan Antonio Morente-Molinera,et al.  Parallel 3D-TLM algorithm for simulation of the Earth-ionosphere cavity , 2013, J. Comput. Phys..

[38]  H. Morkoç,et al.  Transmission-line matrix method for solving the multidimensional continuity equation , 1993 .

[39]  A. Gerlak.  Water , 2013, Ecological Restoration.

[40]  T. Atkinson,et al.  Longitudinal dispersion in natural channels: 2. The roles of shear flow dispersion and dead zones in the River Severn, U.K. , 2000 .

[41]  W. K. Gwarek.  On the Relationship Between TLM and Finite-Difference Methods for Maxwell's Equations (Comments) , 1987 .

[42]  R. Bellasio,et al.  A statistical methodology for the evaluation of long-range dispersion models: an application to the ETEX exercise , 1998 .

[43]  Peter B. Johns,et al.  Numerical solution of 2-dimensional scattering problems using a transmission-line matrix , 1971 .