title: Alles im Fluss: Simulationstechniken der Strömungsmechanik in der Materials Chain
Creators: name: Schröder, Jörg
name: Turek, Stefan
name: Schwarz, Alexander
Publisher: name: DuEPublico: Duisburg-Essen Publications online, University of Duisburg-Essen, Germany
Year: 2016
Subjects: subject: 620
subject: 510

description: Dieser Beitrag handelt von numerischen Strömungssimulationen. Heute, 200 Jahre nach ihrer Formulierung, basieren die Simulationen auf Hochleistungscomputern auf den sogenannten Navier-Stokes-Gleichungen.
description: The numerical simulation of complex
problems in fluid dynamics is
becoming more and more important,
not least due to the recent progresses
in high-performance computing. As
a consequence thereof, the development
of robust and efficient numerical
models and solvers is indispensable.
Today’s object of research
in fluid dynamics focuses on the
description of the perfusion of complex
structures based on the Navier-
Stokes equations. Newtonian as well
as non-Newtonian fluids are the
object of ongoing research. A relatively
new and promising method is
based on the variational approach of
the mixed least-squares finite element
method (LSFEM) combined with
efficient iterative solvers for a massive,
parallel computer architecture.
In the present article, a brief
survey on the fundamentals of fluid
dynamics is given first. In addition,
the challenges of ongoing research
are presented and a possible solution
strategy in terms of the LSFEM
is treated in detail. In the framework
of the MERCUR project of
Schröder, Turek and Schwarz, possible
problem-solving approaches are
demonstrated. We explain the leastsquares
method and its principles in
the context of statistics, as well as its
transferability for constructing finite
elements in the framework of computational
fluid dynamics. Thereby,
two different formulations are
investigated in terms of their performance
and efficiency. In benchmark
problems the influence of different
interpolation spaces for the different
formulations with respect to convergence
and precision is examined.
Furthermore, a numerical example
for non-Newtonian fluids is shown.
The inherent a posteriori error estimator
within the LSFEM is a vast
advantage of the method and can be
applied in adaptive mesh generation.
The future challenges within
the LSFEM are the simulation of
geometrically complex structures
and their interaction with passing/
surrounding fluid flows, i.e. fluidstructure-
interaction (FSI), which
arises in manufacturing engineering,
for example. Along with the perfusion
of (micro)structures, the fluid flow through elastic structures such
as blood vessels in combination with
stents are conceivable problems to
solve. The extremely complex interaction
conditions and the nonlinear
coupling of both regimes (fluid and
solid) are the challenges to meet. In
addition, numerical problems including
high Reynolds numbers due to
high velocities and/or low viscosities
demand a special treatment, which
is not yet included in LSFEMs.
These challenges describe the goals
of ongoing research and the way to
progress for least-squares finite element
methods in combination with
efficient, compatible solvers.
description: UNIKATE: Berichte aus Forschung und Lehre, no. 48Materials Chain: Forschung aus dem UA Ruhr-Profilschwerpunkt, p. 66