Refine
H-BRS Bibliography
- yes (10)
Departments, institutes and facilities
- Institut für Technik, Ressourcenschonung und Energieeffizienz (TREE) (10) (remove)
Document Type
- Conference Object (6)
- Article (1)
- Part of a Book (1)
- Preprint (1)
- Report (1)
Has Fulltext
- no (10)
Keywords
- Approximated Jacobian (2)
- Differential-algebraic equations (1)
- Network simulation (1)
- Order conditions (1)
- ROW methods (1)
- Rosenbrock methods (1)
- Rosenbrock-Wanner Methods (1)
- Theory of Rooted Trees (1)
- W methods (1)
- W-Methods (1)
The simulation of fluid flows is of importance to many fields of application, especially in industry and infrastructure. The modelling equations applied describe a coupled system of non-linear, hyperbolic partial differential equations given by one-dimensional shallow water equations that enable the consistent implementation of free surface flows in open channels as well as pressurised flows in closed pipes. The numerical realisation of these equations is complicated and challenging to date due to their characteristic properties that are able to cause discontinuous solutions.
Die im Folgenden dargestellten wichtigsten Ergebnisse des Teilprojektes 5 "Mathematische Beschreibung der relevanten physikalischen Prozesse und numerische Simulation von Wasseraufbereitung und -verteilung" beziehen sich auf die Arbeitspakete 2 "Daten und Methoden zum Modellaufbau, zur Zustandsschätzung, Prognose und Bewertung" und 3 "Physikalische Modelle und Numerische Verfahren".
Since being introduced in the sixties and seventies, semi-implicit RosenbrockWanner (ROW) methods have become an important tool for the timeintegration of ODE and DAE problems. Over the years, these methods have been further developed in order to save computational effort by regarding approximations with respect to the given Jacobian [5], reduce effects of order reduction by introducing additional conditions [2, 4] or use advantages of partial explicit integration by considering underlying Runge-Kutta formulations [1]. As a consequence, there is a large number of different ROW-type schemes with characteristic properties for solving various problem formulations given in literature today.