Monotone difference approximations for the simulation of clarifier-thickener units

Computing and Visualization in Science

Volumn 6, Issue 2-3, 2004, Pages 83-91

  Burger R ^a   Karlsen, K H ^b,c   Risebro, N H ^c   Towers, J D ^d  

^a UNIVERSITY OF STUTTGART   (Germany)

^b UNIVERSITY OF BERGEN   (Norway)

^c UNIVERSITY OF OSLO   (Norway)

^d MiraCosta College   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTER SCIENCE; VISUALIZATION;

CLARIFIER-THICKENER UNITS; DIFFERENCE APPROXIMATION; ITS APPLICATIONS; NONCONVEX; SCALAR CONSERVATION LAWS; WEAK SOLUTION;

INITIAL VALUE PROBLEMS;

EID: 21244437970     PISSN: 14329360     EISSN: 14330369     Source Type: Journal    
DOI: 10.1007/s00791-003-0112-1     Document Type: Article

References (17)

1. Bürger, R., Karlsen, K.H., Klingenberg, C., Risebro, N.H.: A front tracking approach to a model of continuous sedimentation in ideal clarifier-Thickener units, Nonlin. Anal. Real World Appl. 4, 457-481 (2003)
2. Bürger, R., Karlsen, K.H., Risebro, N.H., Towers, J.D.: Numerical methods for the simulation of continuous sedimentation in ideal clarifier-Thickener units. Int. J. Mineral Process., to appear
3. Bürger, R., Karlsen, K.H., Risebro, N.H., Towers, J.D.: On a model for continuous sedimentation in vessels with discontinuous crosssectional area. In: Hou, T.Y. and Tadmor, E. (eds.), Hyperbolic Problems: Theory, Numerics, Applications. Proceedings of the Ninth International Conference on Hyperbolic Problems held in Cal-Tech, Pasadena, March 25-29, 2002. Berlin: Springer-Verlag (2003), 397-406
4. Bürger, R., Karlsen, K.H., Risebro, N.H., Towers, J.D.: Wellposedness in BVt and convergence of a difference scheme for continuous sedimentation in ideal clarifier-Thickener units. Numer. Math., to appear
5. Bustos, M.C., Concha, F., Bürger, R., Tory, E.M.: Sedimentation and Thickening: Phenomenological Foundation and Mathematical Theory. Dordrecht: Kluwer Acad. Publ. 1999
6. Chancelier, J.P., Cohen de Lara, M., Joannis, C., Pacard, F.: New insights in dynamic modeling of a secondary settler-I. Flux theory and steady-states analysis, Wat. Res. 31, 1847-1856 (1997)
7. Diehl, S.: Dynamic and steady-state behavior of continuous sedimentation, SIAM J. Appl. Math. 57, 991-1018 (1997)
8. Engquist, B., Osher, S.: Stable and entropy-satisfying approximations for transonic flow calculations. Math. Comp. 34, 45-75 (1980)
9. Gimse, T., Risebro, N.H.: Solution of the Cauchy problem for a conservation law with a discontinuous flux function, SIAM J. Math. Anal. 23, 635-648 (1992)
10. Holden, H., Risebro, N.H.: Front tracking for conservation laws. New York: Springer-Verlag 2002
11. Kružkov, S.N.: First order quasilinear equations in several independent variables, Math. USSR Sb. 10, 217-243 (1970)
12. Kynch, G.J.: A theory of sedimentation, Trans. Faraday Soc. 48, 166-176 (1952)
13. Mochon, S.: An analysis of the traffic on highways with changing surface conditions, Math. Modelling 9, 1-11 (1987)
14. Temple, B.: Global solution of the Cauchy problem for a 2×2 nonstrictly hyperbolic system of conservation laws, Adv. Appl. Math. 3, 335-375 (1982)
15. Towers, J.D.: Convergence of a difference scheme for conservation laws with a discontinuous flux, SIAM J. Numer. Anal. 38, 681-698 (2000)
16. Towers, J.D.: A difference scheme for conservation laws with a discontinuous flux -The nonconvex case, SIAM J. Numer. Anal. 39, 1197-1218 (2001)
17. White, D.A., Verdone, N.: Numerical modelling of sedimentation processes, Chem. Eng. Sci. 55, 2213-2222 (2000)