A front tracking approach to a model of continuous sedimentation in ideal clarifier-thickener units

Nonlinear Analysis: Real World Applications

Volumn 4, Issue 3, 2003, Pages 457-481

  Burger R ^a   Karlsen, K H ^b   Klingenberg, C ^c   Risebro, N H ^d  

^a UNIVERSITY OF STUTTGART   (Germany)

^b UNIVERSITY OF BERGEN   (Norway)

^c UNIVERSITY OF WÜRZBURG   (Germany)

^d UNIVERSITY OF OSLO   (Norway)

Author keywords

Conservation law; Continuous sedimentation; Convergence; Discontinuous flux; Front tracking; Numerical example; Weak solution

Indexed keywords

EID: 0037412050     PISSN: 14681218     EISSN: None     Source Type: Journal    
DOI: 10.1016/S1468-1218(02)00071-8     Document Type: Article

References (31)

1. N.G. Barton, C.-H. Li, S.J. Spencer, Control of a surface of discontinuity in continuous thickeners, J. Austral. Math. Soc. Ser. B 33 (1992) 269-289.
2. A. Bressan, Global solutions to systems of conservation laws by wave-front tracking, J. Math. Anal. Appl. 170 (1992) 414-432.
3. 1 stability estimates for n × n conservation laws, Arch. Rat. Mech. Anal. 149 (1999) 1-22.
4. R. Bürger, E.M. Tory, On upper rarefaction waves in batch settling, Powder Technol. 108 (2000) 74-87.
5. M.C. Bustos, F. Concha, Settling velocities of particulate systems: 10. A numerical method for solving Kynch sedimentation processes, Int. J. Mineral Process. 57 (1999) 185-203.
6. M.C. Bustos, F. Concha, R. Bürger, E.M. Tory, Sedimentation and Thickening, Kluwer Academic Publishers, Dordrecht, 1999.
7. M.C. Bustos, F. Concha, W.L. Wendland, Global weak solutions to the problem of continuous sedimentation of an ideal suspension, Math. Meth. Appl. Sci. 13 (1990) 1-22.
8. M.C. Bustos, F. Paiva, W.L. Wendland, Entropy boundary conditions in the theory of sedimentation of ideal suspensions, Math. Meth. Appl. Sci. 19 (1996) 679-697.
9. J.P. Chancelier, M. Cohen de Lara, F. Pacard, Analysis of a conservation PDE with discontinuous flux: a model of settler, SIAM J. Math. Appl. 54 (1994) 954-995.
10. F. Concha, A. Barrientos, M.C. Bustos, Phenomenological model of high capacity thickening, in: Proceedings of the 19th International Mineral Processing Congress (XIX IMPC), San Francisco, 1995, pp. 75-79 (Chapter 14).
11. C.M. Dafermos, Polygonal approximations of solutions to the initial value problem for a conservation law, J. Math. Anal. Appl. 38 (1972) 33-41.
12. S. Diehl, On scalar conservation laws with point source and discontinuous flux function, SIAM J. Math. Anal. 26 (1995) 1425-1451.
13. S. Diehl, A conservation law with point source and discontinuous flux function modelling continuous sedimentation, SIAM J. Appl. Math. 56 (1996) 388-419.
14. S. Diehl, Dynamic and steady-state behavior of continuous sedimentation, SIAM J. Appl. Math. 57 (1997) 991-1018.
15. S. Diehl, On boundary conditions and solutions for ideal thickener-clarifier units, Chem. Eng. J. 80 (2000) 119-133.
16. R.J. DiPerna, Global existence of solutions to nonlinear systems of conservation laws, J. Diff. Eqns. 20 (1976) 187-212.
17. T. Gimse, N.H. Risebro, Riemann problems with a discontinuous flux function, in: Proceedings of the Third Conf. Hyp. Problems, Uppsala, Sweden, 1990.
18. T. Gimse, N.H. Risebro, Solution of the Cauchy problem for a conservation law with a discontinuous flux function, SIAM J. Math. Anal. 23 (1992) 635-648.
19. H. Holden, L. Holden, R. Høegh-Krohn, A numerical method for first order nonlinear scalar conservation laws in one dimension, Comp. Math. Appl. 15 (1988) 595-602.
20. H. Holden, N.H. Risebro, Front Tracking for Conservation Laws, Springer-Verlag, New York, 2002.
21. C. Klingenberg, N.H. Risebro, Convex conservation laws with discontinuous coefficients, Comm. PDE 20 (1995) 1959-1990.
22. C. Klingenberg, N.H. Risebro, Stability of a resonant system of conservation laws modeling polymer flow with gravitation, J. Diff. Eqns. 170 (2001) 344-380.
23. M. Kunik, A numerical method for some initial-value problems of one scalar hyperbolic conservation law, Math. Meth. Appl. Sci. 15 (1992) 495-509.
24. M. Kunik, A solution formula for a non-convex scalar hyperbolic conservation law with monotone initial data, Math. Meth. Appl. Sci. 16 (1993) 895-902.
25. G.J. Kynch, A theory of sedimentation, Trans. Faraday Soc. 48 (1952) 166-176.
26. O. Lev, E. Rubin, M. Sheintuch, Steady state analysis of a continuous clarifier-thickener system, AIChE J. 32 (1986) 1516-1525.
27. C.A. Petty, Continuous sedimentation of a suspension with a nonconvex flux law, Chem. Eng. Sci. 30 (1975) 1451-1458.
28. N.H. Risebro, A front-tracking alternative to the random choice method, Proc. Amer. Math. Soc. 117 (1993) 1125-1139.
29. N.H. Risebro, A. Tveito, Front tracking applied to a nonstrictly hyperbolic system of conservation laws, SIAM J. Sci. Stat. Comput. 12 (1991) 1401-1419.
30. N.H. Risebro, A. Tveito, A front tracking method for conservation laws in one dimension, J. Comp. Phys. 101 (1992) 130-139.
31. B. Temple, Global solution of the Cauchy problem for a 2 × 2 non-strictly hyperbolic system of conservation laws, Adv. Appl. Math. 3 (1982) 335-375.