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Original Articles

A simulation model for settling tanks with varying cross-sectional area

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References

  • Adimurthi, Jaffré, J., and Veerappa Gowda, G. D. (2004). Godunov-type methods for conservation laws with a flux function discontinuous in space, SIAM J. Numer. Anal. 42(1), 179–208.
  • Bürger, R., Careaga, J., and Diehl, S. (2017). Entropy solutions of a scalar conservation law modelling sedimentation in vessels with varying cross-sectional area, SIAM J. Appl. Math. 77(2), 789–811.
  • Bürger, R., Damasceno, J. J. R., and Karlsen, K. H. (2004). A mathematical model for batch and continuous thickening of flocculated suspensions in vessels with varying cross-section, Int. J. Miner. Process. 73, 183–208.
  • Bürger, R., Diehl, S., Farås, S., and Nopens, I. (2012a). On reliable and unreliable numerical methods for the simulation of secondary settling tanks in wastewater treatment, Comput. Chem. Eng. 41, 93–105.
  • Bürger, R., Diehl, S., Farås, S., Nopens, I., and Torfs, E. (2013). A consistent modelling methodology for secondary settling tanks: A reliable numerical method, Water Sci. Technol. 68(1), 192–208.
  • Bürger, R., Diehl, S., and Nopens, I. (2011). A consistent modelling methodology for secondary settling tanks in wastewater treatment, Water Res. 45(6), 2247–2260.
  • Bürger, R., Karlsen, K. H., and Towers, J. D. (2005). A model of continuous sedimentation of flocculated suspensions in clarifier-thickener units, SIAM J. Appl. Math. 65, 882–940.
  • Bürger, R., Ruiz-Baier, R., and Torres, H. (2012b). A stabilized finite volume element formulation for sedimentation-consolidation processes, SIAM J. Sci. Comput. 34, B265–B289.
  • Chancelier, J.-Ph., Cohen de Lara, M., and Pacard, F. (1994). Analysis of a conservation PDE with discontinuous flux: A model of settler, SIAM J. Appl. Math. 54(4), 954–995.
  • De Clercq, J., Devisscher, M., Boonen, I., Vanrolleghem, P. A., and Defrancq, J. (2003). A new one-dimensional clarifier model – Verification using full-scale experimental data, Water Sci. Technol. 47, 105–112.
  • Diehl, S. (1996). A conservation law with point source and discontinuous flux function modelling continuous sedimentation, SIAM J. Appl. Math. 56(2), 388–419.
  • Diehl, S. (1997). Dynamic and steady-state behavior of continuous sedimentation, SIAM J. Appl. Math. 57(4), 991–1018.
  • Diehl, S. (2015). Numerical identification of constitutive functions in scalar nonlinear convection–diffusion equations with application to batch sedimentation, Appl. Num. Math. 95, 154–172.
  • Diehl, S., Farås, S., and Mauritsson, G. (2015). Fast reliable simulations of secondary settling tanks in wastewater treatment with semi-implicit time discretization, Comput. Math. Appl. 70(4), 459–477.
  • Dill, L. H., and Hajjafar, A. (2007). A numerical solution for the anomalous sedimentation of a small Brownian sphere in a vertical cylinder of periodically varying radius, Chem. Eng. Commun. 194(1), 50–68.
  • Fatoorehchi, H., and Abolghasemi, H. (2012). Investigation of nonlinear problems of heat conduction in tapered cooling fins via symbolic programming, Appl. Appl. Math. 7(2), 717–734.
  • Fatoorehchi, H., and Abolghasemi, H. (2013). Improving the differential transform method: A novel technique to obtain the differential transforms of nonlinearities by the Adomian polynomials, Appl. Math. Model. 37(8), 6008–6017.
  • Fatoorehchi, H. and Abolghasemi, H. (2016). Series solution of nonlinear differential equations by a novel extension of the Laplace transform method, Int. J. Comput. Math. 93(8), 1299–1319.
  • Fatoorehchi, H., Abolghasemi, H., and Zarghami, R. (2015). Analytical approximate solutions for a general nonlinear resistor-nonlinear capacitor circuit model, Appl. Math. Model. 39(19), 6021–6031.
  • Folens, K., Van Hulle, S., Vanhaecke, F., and Du Laing, G. (2016). Chemical fractionation and speciation modelling for optimization of ion-exchange processes to recover palladium from industrial wastewater, Water Sci. Technol. 73(7), 1738–1745.
  • Goličnik, M. (2016). Solution of the extended Michaelis-Menten equation for enzyme kinetics with spontaneous substrate depletion using the Adomian decomposition method, MATCH Commun. Math. Comput. Chem. 75, 613–626.
  • Jain, R., Arekar, K., and Dubey, R. S. (2017). Study of Bergman’s minimal blood glucose-insulin model by Adomian decomposition method, J. Inf. Optim. Sci. 38(1), 133–149.
  • Jiao, H., Wu, A., Wang, H., Zhong, S., Ruan, R., and Yin, S. (2013). The solids concentration distribution in the deep cone thickener: A pilot scale test, Korean J. Chem. Eng. 30(2), 262–268.
  • Liao, W., Tordeux, A., Seyfried, A., Chraibi, M., Drzycimski, K., Zheng, X., and Zhao, Y. (2016). Measuring the steady state of pedestrian flow in bottleneck experiments, Phys. A Stat. Mech. Appl. 461, 248–261.
  • Mekheimer, Kh. S. and El Kot, M. A. (2010). Suspension model for blood flow through arterial catheterization, Chem. Eng. Commun. 197(9), 1195–1214.
  • Park, J. and Craggs, R. (2014). Effect of algal recycling rate on the performance of pediastrum boryanum dominated wastewater treatment high rate algal pond, Water Sci. Technol. 70(8), 1299–1306.
  • Poloni, M., Winterbone, D. E., and Nichols, J. R. (1987). Comparison of unsteady flow calculations in a pipe by the method of characteristics and the two-step differential Lax-Wendroff method, Int. J. Mech. Sci. 29(5), 367–378.
  • Rawashdeh, M. and Maitama, S. (2017). Finding exact solutions of nonlinear PDEs using the natural decomposition method, Math. Methods Appl. Sci. 40(1), 223–236.
  • Samstag, R. W., Ducoste, J. J., Griborio, A., Nopens, I., Batstone, D. J., Wicks, J. D., Saunders, S., Wicklein, E. A., Kenny, G., and Laurent, J. (2016). CFD for wastewater treatment: An overview, Water Sci. Technol. 74(3), 549–563.
  • Silva, T. A., Freitas, K. A., and Damasceno, J. J. R. (2003). Experimental evaluation of conical-cylindrical thickeners operanting with aqueous barium sulfate suspensions, Mater. Sci. Forum 416–418, 731–736.
  • Stepova, N. and Kalugin, Yu. I. (2011). Mathematical modeling of a secondary clarifier with cone-shaped bottom, Int. J. Fluid Mech. Res. 38(5), 458–478.
  • Thanh, M. D. (2009). The Riemann problem for a nonisentropic fluid in a nozzle with discontinuous cross-sectional area, SIAM J. Appl. Math. 69(6), 1501–1519.
  • Torfs, E., Balemans, S., Locatelli, F., Diehl, S., Bürger, R., Laurent, J., Françis, P., and Nopens, I. (2017). On constitutive functions for hindered settling velocity in 1-d settler models: Selection of appropriate model structure, Water Res. 110, 38–47.
  • Torfs, E., Maere, T., Bürger, R., Diehl, S., and Nopens, I. (2015). Impact on sludge inventory and control strategies using the benchmark simulation model no. 1 with the Bürger-Diehl settler model, Water Sci. Technol. 71(10), 1524–1535.
  • van der Steen, P., Rahsilawati, K., Rada-Ariza, A., Lopez-Vazquez, C., and Lens, P. (2015). A new photo-activated sludge system for nitrification by an algal-bacterial consortium in a photo-bioreactor with biomass recycle, Water Sci. Technol. 72(3), 443–450.
  • Verdickt, L., Smets, I., and Van Impe, J. (2005). Sensitivity analysis of a one-dimensional convection-diffusion model for secondary settling tanks, Chem. Eng. Commun. 192, 1567–1585.
  • Watts, R. W., Svoronos, S. A., and Koopman, B. (1996). One-dimensional clarifer model with sludge blanket heights, J. Environ. Eng. 122(12), 1094–1100.
  • White, D. A. and Verdone, N. (2000). Numerical modelling of sedimentation processes, Chem. Eng. Sci. 55, 2213–2222.

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