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All issues Volume 57 / No 5 (September-October 2023) ESAIM: M2AN, 57 5 (2023) 2931-2976 References
Open Access
Issue
ESAIM: M2AN
Volume 57, Number 5, September-October 2023
Page(s) 2931 - 2976
DOI https://doi.org/10.1051/m2an/2023068
Published online 19 September 2023
  1. M.M. Amin, M.H. Khiadani (Hajian), A. Fatehizadeh and E. Taheri, Validation of linear and non-linear kinetic modeling of saline wastewater treatment by sequencing batch reactor with adapted and non-adapted consortiums. Desalination 344 (2014) 228–235. [CrossRef] [Google Scholar]
  2. S. Berres, R. Bürger, K.H. Karlsen and E.M. Tory, Strongly degenerate parabolic-hyperbolic systems modeling polydisperse sedimentation with compression. SIAM J. Appl. Math. 64 (2003) 41–80. [Google Scholar]
  3. S. Boscarino, R. Bürger, P. Mulet, G. Russo and L.M. Villada, Linearly implicit IMEX Runge-Kutta methods for a class of degenerate convection-diffusion problems. SIAM J. Sci. Comput. 37 (2015) B305–B331. [CrossRef] [Google Scholar]
  4. M. Breu, A theory of implicit methods for scalar conservation laws. In Hyperbolic Problems: Theory, Numerics, Applications. Springer, Berlin (2003) 377–386. [CrossRef] [Google Scholar]
  5. M. Breu, The implicit upwind method for 1-D scalar conservation laws with continuous fluxes. SIAM J. Numer. Anal. 43 (2005) 970–986. [CrossRef] [MathSciNet] [Google Scholar]
  6. M. Breu and A. Kleefeld, Implicit monotone difference methods for scalar conservation laws with source terms. Acta Math. Vietnam. 45 (2020) 709–738. [CrossRef] [MathSciNet] [Google Scholar]
  7. R. Bürger, F. Concha and K.H. Karlsen, Phenomenological model of filtration processes: 1. Cake formation and expression. Chem. Eng. Sci. 56 (2001) 4537–4553. [CrossRef] [Google Scholar]
  8. R. Bürger, H. Frid and K.H. Karlsen, On a free boundary problem for a strongly degenerate quasi-linear parabolic equation with an application to a model of pressure filtration. SIAM J. Math. Anal. 34 (2002) 611–635. [CrossRef] [MathSciNet] [Google Scholar]
  9. R. Bürger, K.H. Karlsen and J.D. Towers, A model of continuous sedimentation of flocculated suspensions in clarifier-thickener units. SIAM J. Appl. Math. 65 (2005) 882–940. [Google Scholar]
  10. R. Bürger, A. Coronel and M. Sepúlveda, A semi-implicit monotone difference scheme for an initial-boundary value problem of a strongly degenerate parabolic equation modeling sedimentation-consolidation processes. Math. Comp. 75 (2006) 91–112. [Google Scholar]
  11. R. Bürger, S. Diehl and I. Nopens, A consistent modelling methodology for secondary settling tanks in wastewater treatment. Water Res. 45 (2011) 2247–2260. [CrossRef] [Google Scholar]
  12. R. Bürger, J. Careaga, S. Diehl, C. Mejías, I. Nopens, E. Torfs and P.A. Vanrolleghem, Simulations of reactive settling of activated sludge with a reduced biokinetic model. Comput. Chem. Eng. 92 (2016) 216–229. [CrossRef] [Google Scholar]
  13. R. Bürger, S. Diehl and C. Mejías, A difference scheme for a degenerating convection-diffusion-reaction system modelling continuous sedimentation. ESAIM: Math. Model. Numer. Anal. 52 (2018) 365–392. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
  14. R. Bürger, J. Careaga and S. Diehl, A method-of-lines formulation for a model of reactive settling in tanks with varying cross-sectional area. IMA J. Appl. Math. 86 (2021) 514–546. [CrossRef] [MathSciNet] [Google Scholar]
  15. R. Bürger, J. Careaga, S. Diehl and R. Pineda, A moving-boundary model of reactive settling in wastewater treatment. Part 1: Governing equations. Appl. Math. Model. 106 (2022) 390–401. [CrossRef] [MathSciNet] [Google Scholar]
  16. R. Bürger, J. Careaga, S. Diehl and R. Pineda, A moving-boundary model of reactive settling in wastewater treatment. Part 2: Numerical scheme. Appl. Math. Model. 111 (2022) 247–269. [CrossRef] [MathSciNet] [Google Scholar]
  17. R. Bürger, S. Diehl, M.C. Martí and Y. Vásquez, A degenerating convection-diffusion system modelling froth flotation with drainage. IMA J. Appl. Math. 87 (2022) 1151–1190. [CrossRef] [MathSciNet] [Google Scholar]
  18. R. Bürger, J. Careaga, S. Diehl and R. Pineda, A model of reactive settling of activated sludge: Comparison with experimental data. Chem. Eng. Sci. 267 (2023) 118244. [CrossRef] [Google Scholar]
  19. R. Bürger, S. Diehl, M.C. Martí and Y. Vásquez, A difference scheme for a triangular system of conservation laws with discontinuous flux modeling three-phase flows. Netw. Heterog. Media 18 (2023) 140–190. [Google Scholar]
  20. M. Caluwé, D. Daens, R. Blust, L. Geuens and J. Dries, The sequencing batch reactor as an excellent configuration to treat wastewater from the petrochemical industry. Water Sci. Tech. 75 (2016) 793–801. [Google Scholar]
  21. G. Chen, M.C.M. van Loosdrecht, G.A. Ekama and D. Brdjaniovic, Biological Wastewater Treatment, 2nd edition. IWA Publishing, London, UK (2020). [Google Scholar]
  22. G.M. Coclite, S. Mishra and N.H. Risebro, Convergence of an Engquist-Osher scheme for a multi-dimensional triangular system of conservation laws. Math. Comput. 79 (2010) 71–94. [CrossRef] [Google Scholar]
  23. R. Courant, K. Friedrichs and H. Lewy, Über die partiellen Differenzengleichungen der mathematischen Physik. Math. Ann. 100 (1928) 32–74. [Google Scholar]
  24. K. Deimling, Nonlinear Functional Analysis. Springer-Verlag, Berlin (1985). [Google Scholar]
  25. S. Diehl, Continuous sedimentation of multi-component particles. Math. Meth. Appl. Sci. 20 (1997) 1345–1364. [CrossRef] [Google Scholar]
  26. R. Droste and R. Gear, Theory and Practice of Water and Wastewater Treatment, 2nd edition. Wiley, Hoboken, NJ, USA (2019). [Google Scholar]
  27. B. Engquist and S. Osher, One-sided difference approximations for nonlinear conservation laws. Math. Comput. 36 (1981) 321–351. [CrossRef] [Google Scholar]
  28. S. Evje and K.H. Karlsen, Degenerate convection-diffusion equations and implicit monotone difference schemes. In Hyperbolic Problems: Theory, Numerics, Applications, Vol. I (Zürich, 1998), Vol. 129 of Internat. Ser. Numer. Math. Birkhäuser, Basel (1999) 285–294. [CrossRef] [Google Scholar]
  29. R. Eymard, T. Gallouët and R. Herbin, Finite volume methods. In Handbook of Numerical Analysis, Vol. VII, Handb. Numer. Anal., VII, North-Holland, Amsterdam (2000) 713–1020. [Google Scholar]
  30. M. Henze, W. Gujer, T. Mino and M.C.M. van Loosdrecht, Activated Sludge Models ASM1, ASM2, ASM2d and ASM3. IWA Scientific and Technical Report No. 9. IWA Publishing, London, UK (2000). [Google Scholar]
  31. J.S. Hesthaven, Numerical methods for conservation Laws. In Vol. 18 of Computational Science & Engineering. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA (2018). [Google Scholar]
  32. H. Holden, K.H. Karlsen and N.H. Risebro, On uniqueness and existence of entropy solutions of weakly coupled systems of nonlinear degenerate parabolic equations. Electron. J. Differ. Equ. 2003 (2003) 46. [Google Scholar]
  33. Z. Hu, R.A. Ferraina, J.F. Ericson, A.A. MacKay and B.F. Smets, Biomass characteristics in three sequencing batch reactors treating a wastewater containing synthetic organic chemicals. Water Res. 39 (2005) 710–720. [CrossRef] [Google Scholar]
  34. W. Hundsdorfer and J. Verwer, Numerical solution of time-dependent advection-diffusion-reaction equations, In Vol. 33 of Springer Series in Computational Mathematics. Springer-Verlag, Berlin (2003). [CrossRef] [Google Scholar]
  35. Y. Jiang and Z. Xu, Parametrized maximum principle preserving limiter for finite difference WENO schemes solving convectiondominated diffusion equations. SIAM J. Sci. Comput. 35 (2013) A2524–A2553. [CrossRef] [Google Scholar]
  36. K.H. Karlsen and J.D. Towers, Convergence of monotone schemes for conservation laws with zero-flux boundary conditions. Adv. Appl. Math. Mech. 9 (2017) 515–542. [Google Scholar]
  37. G. Kirim, E. Torfs and P.A. Vanrolleghem, An improved 1d reactive BürgerDiehl settler model for secondary settling tank denitrification. Water Environ. Res. 94 (2022) e10825. [Google Scholar]
  38. R.J. LeVeque, Finite Volume Methods for Hyperbolic Problems. Cambridge Texts in Applied Mathematics. Cambridge University Press, Cambridge (2002). [Google Scholar]
  39. J. Makinia and E. Zaborowska, Mathematical Modelling and Computer Simulation of Activated Sludge Systems, 2nd edition. IWA Publishing, London, UK (2020). [CrossRef] [Google Scholar]
  40. L. Metcalf and H.P. Eddy, Wastewater Engineering. Treatment and Resource Recovery, 5th edition. McGraw-Hill, New York, USA (2014). [Google Scholar]
  41. T. Popple, J. Williams, E. May, G. Mills and R. Oliver, Evaluation of a sequencing batch reactor sewage treatment rig for investigating the fate of radioactively labelled pharmaceuticals: Case study of propranolol. Water Res. 88 (2016) 83–92. [CrossRef] [Google Scholar]
  42. B. Song, Z. Tian, R. van der Weijden, C. Buisman and J. Weijma, High-rate biological selenate reduction in a sequencing batch reactor for recovery of hexagonal selenium. Water Res. 193 (2021) 116855. [CrossRef] [Google Scholar]
  43. E. Torfs, S. Balemans, F. Locatelli, S. Diehl, R. Bürger, J. Laurent, P. François and I. Nopens, On constitutive functions for hindered settling velocity in 1-d settler models: Selection of appropriate model structure. Water Res. 110 (2017) 38–47. [CrossRef] [Google Scholar]
  44. S. Wang and C.K. Gunsch, Effects of selected pharmaceutically active compounds on treatment performance in sequencing batch reactors mimicking wastewater treatment plants operations. Water Res. 45 (2011) 3398–3406. [CrossRef] [Google Scholar]

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