International Scientific Journal


In this study, Network Simulation Method (NSM) is applied to solve a onedimensional solute transfer problem governed by Transient Storage (TS) model in a mountain stream including dead zones. In this computational method, for each node of the discretized domain, the terms of governing equation are substituted by the equivalent electrical devices which are connected to each other based on Kirchhoff’s current law. Finally, the total electric circuit is solved using an appropriate electrical code to obtain the unknown value at the nodes. Because no analytical solutions for this model have been presented so far, to verify NSM, the problem is solved by Finite Volume Method (FVM), as well. According to the results, estimations made by NSM and FVM are in good agreement. Further, NSM is easier in implementation, especially in implementation of boundary conditions, and faster than FVM in computation. Therefore, in the case of one-dimensional mass transfer problems with a set of coupled equations, NSM is recommended to be used as an efficient alternative to numerical methods.
PAPER REVISED: 2019-07-27
PAPER ACCEPTED: 2019-07-31
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2019, VOLUME 23, ISSUE Supplement 6, PAGES [S1917 - S1927]
  1. West, P. C., et al., Feeding the world and protecting biodiversity, Encyclopedia of biodiversity, 2nd edition, Academic Press, Waltham, MA, USA, pp. 426-434, 2013
  2. Elder, J. W., The dispersion of marked fluid in turbulent shear flow, Journal of fluid mechanics, 5 (1959), 4, pp. 544-560
  3. Czernuszenko, W., Dispersion of pollutants in rivers, Hydrological sciences journal, 32 (1987), 1, pp. 59-67
  4. Beltaos, S., Day, T. J., A field study of longitudinal dispersion, Canadian Journal of Civil Engineering, 5 (1978), 4, pp. 572-585
  5. Bencala, K. E., et al., Characterization of transport in an acidic and metal-rich mountain stream based on a lithium tracer injection and simulations of transient storage, Water Resources Research, 26 (1990), 5, pp. 989-1000
  6. Day, T. J.,Longitudinal dispersion in natural channels, Water Resources Research, 11 (1975), 6, pp. 909-918
  7. O'Connor, B. L., et al., Predictive modeling of transient storage and nutrient uptake: Implications for stream restoration, Journal of Hydraulic Engineering, 136 (2009), 12, pp. 1018-1032
  8. Bencala, K. E., Simulation of solute transport in a mountain pool-and-riffle stream with a kinetic mass transfer model for sorption, Water Resources Research, 19 (1983), 3, pp. 732-738
  9. Harvey, J. W., et al., Evaluating the reliability of the stream tracer approach to characterize stream subsurface water exchange, Water resources research, 32 (1996), 8, pp. 2441-2451
  10. Nordin, C. F., Troutman, B. M., Longitudinal dispersion in rivers: The persistence of skewness in observed data, Water Resources Research, 16 (1980), 1, pp. 123-128
  11. Runkel, R. L., One-dimensional transport with inflow and storage (OTIS): A solute transport model for streams and rivers. Water-Resources Investigations Report No. 98, p. 4018, 1998
  12. Singh, S. K., Treatment of stagnant zones in riverine advection-dispersion, Journal of Hydraulic Engineering, 129 (2003), 2, pp. 470-473
  13. Fernald, A. G., et al., Transient storage and hyporheic flow along the Willamette River, Oregon: Field measurements and model estimates, Water Resources Research, 37 (2001), 6, pp. 1681-1694
  14. Zand, S. M., et al., Solute transport and modeling of water quality in a small stream, Journal of Research of the U.S. Geological Survey, 4 (1976), 2, pp. 233-240
  15. Bencala, K. E., Walters R. A., Simulation of solute transport in a mountain pool-and-riffle stream: A transient storage model, Water Resources Research, 19 (1983), 3, pp. 718-724
  16. Chapra, S. C., Wilcock, R. J., Transient storage and gas transfer in lowland stream, Journal of environmental engineering, 126 (2000), 8, pp. 708-712
  17. DeAngelis, D. L., et al., Modelling nutrient-periphyton dynamics in streams: the importance of transient storage zones, Ecological Modelling, 80 (1995), 2-3, pp. 149-160
  18. Gooseff, M. N., et al., Relating transient storage to channel complexity in streams of varying land use in Jackson Hole, Wyoming, Water Resources Research, 43 (2007), 1
  19. Wagner, B. J., Harvey, J. W., Experimental design for estimating parameters of rate-limited mass transfer: Analysis of stream tracer studies, Water Resources Research, 33 (1997), 7, pp. 1731-1741
  20. Briggs, M. A., et al., A method for estimating surface transient storage parameters for streams with concurrent hyporheic storage, Water Resources Research, 45 (2009), 4
  21. Barati Moghaddam, et al., A comprehensive one-dimensional numerical model for solute transport in rivers, Hydrology and Earth System Sciences, 21 (2017), 1, pp. 99-116
  22. Alhama,F., Campo,A.,Utilization of the PSPICE code for unsteady thermal response of composite walls in a heat transfer course, International Journal of Mechanical Engineering Education, 31 (2003), 4, pp. 359-369
  23. Alhama, F., Fernández, C. G., Transient thermal behaviour of phase-change processes in solid foods with variable thermal properties, Journal of Food Engineering, 54 (2002), 4, pp. 331-336
  24. Poza, A. J., et al., A Network Simulation Method for Numerical Solution of the Nonlinear Poisson-Boltzmann Equation for a Spheroidal Surface, Journal of colloid and interface science, 219 (1999), 2, pp. 241-249
  25. Manteca, I. A., et al., FATSIM‐A: An educational tool based on electrical analogy and the code PSPICE to simulate fluid flow and solute transport processes, Computer Applications in Engineering Education, 22 (2014), 3, pp. 516-528
  26. Del Cerro Velázquez, F., et al., A powerful and versatile educational software to simulate transient heat transfer processes in simple fins, Computer Applications in Engineering Education, 16 (2008), 1, pp. 72-82
  27. Garcia-Hernandez, et al., Application of the network method to simulation of a square scheme with Butler-Volmer charge transfer, Journal of Electroanalytical Chemistry, 424 (1997), 1-2, pp. 207-212
  28. Horno, J., et al., The network method for solutions of oscillating reaction-diffusion systems, Journal of Computational Physics, 118 (1995), 2, pp. 310-319
  29. Serna, J., et al., Application of network simulation method to viscous flows: The nanofluid heated lid cavity under pulsating flow, Computers & Fluids, 91 (2014), pp. 10-20.
  30. Wyatt Jr, J. L., et al., Network modelling of reaction-diffusion systems and their numerical solution using SPICE, Chemical Engineering Science, 35 (1980), 10, pp. 2115-2127
  31. Hite, G. E., Analog model of diffusion in bays and estuaries. Marine environmental research, 33 (1992), 1, pp. 75-82
  32. Meddah, S., et al., Pollutant dispersion modeling in natural streams using the transmission line matrix method, Water, 7 (2015), 9, pp. 4932-4950
  33. Caravaca, M., et al., The network simulation method: a useful tool for locating the kinetic-thermodynamic switching point in complex kinetic schemes, Physical Chemistry Chemical Physics, 16 (2014), 46, pp. 25409-25420
  34. Ataieyan, A., et al., One-dimensional simulation of mass transfer in a river with dead zones using network simulation method, Proceedings (Dr. Bayram M., Dr. Secer A., ICAAMM2019 Abstract book), 8th International conference on applied analysis and mathematical modeling, Istanbul, Turkey, 2019, pp. 29-30
  35. Jackman, A. P., et al., Transport and concentration controls for chloride, strontium, potassium and lead in Uvas Creek, a small cobble-bed stream in Santa Clara County, California, USA: 2. Mathematical modeling, Journal of Hydrology, 75 (1984), 1-4, pp. 111-141
  36. Horno Montijano, J., Network simulation method, Research Signpost, Jaén, Spain, 2002
  37. Tuinenga, P. W., SPICE: a guide to circuit simulation and analysis using PSpice, Prentice Hall PTR Upper Saddle River, NJ, USA, 1988
  38. Versteeg, H. K., Malalasekera, W., An introduction to computational fluid dynamics: the finite volume method, Pearson Education, London, 2007
  39. Avanzino, R. J., et al., Results of a solute transport experiment at Uvas Creek, September 1972, Report No. 84-236, US Geological Survey, 1984

© 2021 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence