Abstract
River alarm systems are designed for the forecasting of water stages during floods or low flow conditions or the prediction of the transport of pollution plumes. The basic model equations are introduced and a Method of Lines approach for their numerical solution is discussed. The approach includes adaptive space-mesh strategies and a Rosenbrock-Wanner scheme for the time integration. It fits into a PC environment and fulfills the requirements on an implementation within river alarm systems.
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References
Berzins, M., Furzeland, R.M.: A user’ manual for sprint — A versatile software package for solving systems of algebraic ordinary and partial differential equations: Part 1 (TNER.85.058), 2 (TNER.86.050) and 3 (TNER.88.034), Thornton Research Centre, Shell Maatschappij ( 1985, 1986, 1989 ).
Flaherty, J.E., et al: Adaptive methods for partial differential equations. SIAM Publications (1989).
Hairer, E., Wanner, G.: Solving ordinary differential equations II, Springer Series in Computational Mathematics, Berlin, Heidelberg (1991). 19
Hyman, J.M.: Moving mesh methods for partial differential equations, in Mathematics Applied to Science, eds. J. Goldstein, S. Rosencrans, G.Sod, Academic Press, 129 - 154 (1988).
Kautsky, J., Nichols, N. K.: Equidistributing meshes with constraints. SIAM J. Sci. Stat. Comput. 1, 499 - 511 (1980).
Rentrop, P., Steinebach, G.: Model and numerical techniques for the alert system of river Rhine. To appear in Surveys Math. Industry.
Ostermann, A., Roche, M.: Rosenbrock methods for partial differential equations and fractional orders of convergence. SIAM J. Numer. Anal. 30, 1084 - 1098 (1993).
Petzold, L.R.: Observations on an adaptive moving grid method for one-dimensional systems of partial differential equations. Applied Numer. Math. 3, 347 - 360 (1987).
Sanz-Serna, J.M., Verwer, J.G., Hundsdorfer, W.H.: Convergence and order reduction of Runge-Kutta schemes applied to evolutionary problems in partial differential equations. Numer. Math. 50, 405 - 418 (1986).
Spreafico, M., van Mazijk, A.: Alarmmodell Rhein. Ein Modell für die operationelle Vorhersage des Transportes von Schadstoffen im Rhein. KHRBericht Nr. I-12, Lelystad (1993).
Steinebach, G.: Die Linienmethode und ROW-Verfahren zur Abfluß-und Prozeßsimulation in Fließgewässern am Beispiel von Rhein und Mosel. TH Darmstadt, Thesis (1995).
Steinebach, G.: Order-reduction of ROW-methods for DAEs and method of lines applications. To appear in Numer. Math.
Stoker, J. J.: Water Waves, the mathematical theory with applications. Interscience Publishers Inc., New York (1957).
Verwer, J.G. et al: A moving grid method for one-dimensional PDEs based on the method of lines. In Flaherty, J.E., et al: Adaptive Methods for Partial Differential Equations, SIAM Publications, 160–175 (1989).
Vreugdenhil, C.B.: Computational hydraulics, an introduction. Springer, Berlin (1989).
Walsteijn, F. H.: Essentially non-oscillatory (ENO) schemes. In Vreugdenhil, C.B., Koren, B.: Numerical methods for advection-diffusion problems. Vieweg Notes on Numerical Fluid Mechanics, 45, 27-54, Braunschweig (1993).
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© 1997 B. G. Teubner Stuttgart
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Rentrop, P., Steinebach, G. (1997). A Method of Lines Approach for River Alarm Systems. In: Brøns, M., Bendsøe, M.P., Sørensen, M.P. (eds) Progress in Industrial Mathematics at ECMI 96. European Consortium for Mathematics in Industry, vol 9. Vieweg+Teubner Verlag, Wiesbaden. https://doi.org/10.1007/978-3-322-96688-9_1
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DOI: https://doi.org/10.1007/978-3-322-96688-9_1
Publisher Name: Vieweg+Teubner Verlag, Wiesbaden
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