Authors: Jendrny, Robert
Mierka, Otto
Münster, Raphael
Turek, Stefan
Title: A monolithic operator-adaptive Newton-Multigrid solver for Navier-Stokes Equations in 3D
Language (ISO): en
Abstract: The aim of this paper is to describe a new, fast and robust solver for 3D flow problems which are described by the incompressible Navier-Stokes equations. The correspondig simulations are done by a monolithic 3D flow solver, i.e. velocity and pressure are solved at the same time. During these simulations the convective part is linearized using two different 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 find 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 flow around a sphere and a cylinder is simulated to analyze the behaviour of the used methods. Since the behaviour of the linearization types is different between each of them, the results caused by varying Reynolds numbers and the arised equations are analyzed concerning the efficiency of each method.
Subject Headings: Navier-Stokes equations
Fixpoint method
Newton method
adaptive Newton
Issue Date: 2019-08
Appears in Collections:Ergebnisberichte des Instituts für Angewandte Mathematik

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