Techn. Universiẗat, Diss., 2002--Darmstadt.

Techn. Universiẗat, Diss., 2004--Darmstadt.

Techn. Universiẗat, Diss., 2004--Berlin.

Zugl.: Aachen, Techn. University, Diss., 2009.

Modern engineering structures should ensure an economic design, construction and operation of structures in compliance with the required safety for persons and the environment. In order to achieve this aim, all contingencies and associated consequences that may possibly occur throughout the life cycle of the considered structure have to be taken into account. Today, the development is often based on decision theory, methods of structural reliability and the modeling of consequences. Failure consequences are one of the significant issues that determine optimal structural reliability. In particular, consequences associated with the failure of structures are of interest, as they may lead to significant indirect consequences, also called follow-up consequences. However, apart from determining safety levels based on failure consequences, it is also crucially important to have effective models for stress forces and maintenance planning ... (aus dem Vorwort)

We present a discretization method of the Navier–Stokes Cahn–Hilliard equations which offers an impressing simplicity, making it easy to implement a scalable parallel code from scratch. The method is based on a special pressure projection scheme with incomplete pressure iterations. The resulting scheme admits solution by an explicit Euler method. Hence, all unknowns decouple, which enables a very simple implementation. This goes along with the opportunity of a straightforward parallelization, for example, by few lines of Open Multi-Processing (OpenMP) or Message Passing Interface (MPI) routines. Using a standard benchmark case of a rising bubble, we show that the method provides accurate results and good parallel scalability. / Wir stellen eine Diskretisierungsmethode der Navier-Stokes-Cahn-Hilliard-Gleichungen vor, welche es erlaubt, mit wenig Aufwand einen einfachen, skalierbar parallelen Code zu implementieren. Die Methode basiert auf einem Druckprojektionsschema mit unvollständigen Druckiterationen was eine Lösung durch eine explizite Euler-Methode erlaubt. Somit sind alle Unbekannten entkoppelt, was eine sehr einfache Implementierung mit einer unkomplizierten Parallelisierung ermöglicht, zum Beispiel durch Open Multi-Processing (OpenMP) oder Message Passing Interface (MPI) Routinen. Anhand eines Standard-Benchmark-Falls einer aufsteigenden Blase zeigen wir, dass die Methode genaue Ergebnisse und eine gute parallele Skalierbarkeit liefert.