A monolithic operator-adaptive Newton-multigrid solver for Navier-stokes equations in 3D / R. Jendrny, O. Mierka, R. Münster, S. Turek
VerfasserJendrny, Robert ; Mierka, Otto ; Münster, Raphael ; Turek, Stefan
ErschienenDortmund : Technische Universität Dortmund, Fakultät für Mathematik, August 2019
Elektronische Ressource
Umfang1 Online-Ressource (23 Seiten) : Illustrationen
SerieErgebnisberichte angewandte Mathematik ; no. 611
SchlagwörterNavier-Stokes-Gleichung / Fixpunkt-Methode / Newton-Verfahren
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A monolithic operator-adaptive Newton-multigrid solver for Navier-stokes equations in 3D [0.82 mb]

The aim of this paper is to describe a new, fast and robust solver for 3D ow problems which are described by the incompressible Navier-Stokes equations. The correspondig simulations are done by a monolithic 3D ow solver, i.e. velocity and pressure are solved at the same time. During these simulations the convective part is linearized using two di erent methods: Fixpoint method and Newton method. The Fixpoint method is working in a quite robust way, but it has a slow convergence depending on the Reynolds number. In contrast, if the Newton method does not fail, the simulations which are done by this linearization converge typically much faster. In the case of the Newton method quadratical convergence is obtained. The challenging part is to nd a method which unites the stability of the Fixpoint method and the fast convergence of the Newton method. For the resulting operator-adaptive Newton method, several numerical examples are considered: The ow around a sphere and a cylinder is simulated to analyze the behaviour of the used methods. Since the behaviour of the linearization types is di erent between each of them, the results caused by varying Reynolds numbers and the arised equations are analyzed concerning the eciency of each method.

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