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A numerical investigation of velocity-pressure reduced order models for incompressible flows
This report has two main goals. First, it numerically investigates
three velocity-pressure reduced order models (ROMs) for incompressible flows.
The proper orthogonal decomposition (POD) is used to generate the modes. One
method computes the ROM pressure solely based on the velocity POD modes,
whereas the other two ROMs use pressure modes as well. To the best of the
authors knowledge, one of the latter methods is novel. The second goal is to
numerically investigate the impact of the snapshot accuracy on the ROMs
accuracy. Numerical studies are performed on a two-dimensional laminar flow
past a circular obstacle. It turns out that, both in terms of accuracy and
efficiency, the two ROMs that utilize pressure modes are clearly superior to
the ROM that uses only velocity modes. The numerical results also show a
strong correlation of the accuracy of the snap shots with the accuracy of the
ROMs
A numerical investigation of velocity-pressure reduced order models for incompressible flows
This report has two main goals. First, it numerically investigates three velocity-pressure reduced order models (ROMs) for incompressible flows. The proper orthogonal decomposition (POD) is used to generate the modes. One method computes the ROM pressure solely based on the velocity POD modes, whereas the other two ROMs use pressure modes as well. To the best of the authors' knowledge, one of the latter methods is novel. The second goal is to numerically investigate the impact of the snapshot accuracy on the ROMs accuracy. Numerical studies are performed on a two-dimensional laminar flow past a circular obstacle. It turns out that, both in terms of accuracy and efficiency, the two ROMs that utilize pressure modes are clearly superior to the ROM that uses only velocity modes. The numerical results also show a strong correlation of the accuracy of the snap shots with the accuracy of the ROMs
POD model order reduction with space-adapted snapshots for incompressible flows
We consider model order reduction based on proper orthogonal decomposition
(POD) for unsteady incompressible Navier-Stokes problems, assuming that the
snapshots are given by spatially adapted finite element solutions. We propose
two approaches of deriving stable POD-Galerkin reduced-order models for this
context. In the first approach, the pressure term and the continuity equation
are eliminated by imposing a weak incompressibility constraint with respect to
a pressure reference space. In the second approach, we derive an inf-sup stable
velocity-pressure reduced-order model by enriching the velocity reduced space
with supremizers computed on a velocity reference space. For problems with
inhomogeneous Dirichlet conditions, we show how suitable lifting functions can
be obtained from standard adaptive finite element computations. We provide a
numerical comparison of the considered methods for a regularized lid-driven
cavity problem
Numerical investigation of separated transonic turbulent flows with a multiple-time-scale turbulence model
A numerical investigation of transonic turbulent flows separated by curvature and shock wave - boundary layer interaction is presented. The free stream Mach numbers considered are 0.4, 0.5, 0.6, 0.7, 0.8, 0.825, 0.85, 0.875, 0.90, and 0.925. In the numerical method, the conservation of mass equation is replaced by a pressure correction equation for compressible flows and thus incremental pressure is solved for instead of density. The turbulence is described by a multiple-time-scale turbulence model supplemented with a near-wall turbulence model. The present numerical results show that there exists a reversed flow region at all free stream Mach numbers considered whereas various k-epsilon turbulence models fail to predict such a reversed flow region at low free stream Mach numbers. The numerical results also show that the size of the reversed flow region grows extensively due to the shock wave - turbulent boundary layer interaction as the free stream Mach number is increased. These numerical results show that the turbulence model can resolve the turbulence field subjected to extra strains caused by the curvature and the shock wave - turbulent boundary layer interaction and that the numerical method yields a significantly accurate solution for the complex compressible turbulent flow
Validation of a magneto- and ferro-hydrodynamic model for non-isothermal flows in conjunction with Newtonian and non-Newtonian fluids
This work focuses on the validation of a magnetohydrodynamic (MHD) and ferrohydrodynamic
(FHD) model for non-isothermal flows in conjunction with Newtonian and non-
Newtonian fluids. The importance of this research field is to gain insight into the interaction of
non-linear viscous behaviour of blood flow in the presence of MHD and FHD effects, because
its biomedical application such as magneto resonance imaging (MRI) is in the centre of research
interest. For incompressible flows coupled with MHD and FHD models, the Lorentz force and
a Joule heating term appear due to the MHD effects and the magnetization and magnetocaloric
terms appear due to the FHD effects in the non-linear momentum and temperature equations,
respectively. Tzirtzilakis and Loukopoulos [1] investigated the effects of MHD and FHD for
incompressible non-isothermal flows in conjunction with Newtonian fluids in a small rectangular
channel. Their model excluded the non-linear viscous behaviour of blood flows considering
blood as a Newtonian biofluid. Tzirakis et al. [2, 3] modelled the effects of MHD and FHD for
incompressible isothermal flows in a circular duct and through a stenosis in conjunction with
both Newtonian and non-Newtonian fluids, although their approach neglects the non-isothermal
magnetocaloric FHD effects. Due to the fact that there is a lack of experimental data available
for non-isothermal and non-Newtonian blood flows in the presence of MHD and FHD effects,
therefore the objective of this study is to establish adequate validation test cases in order to assess
the reliability of the implemented non-isothermal and non-Newtonian MHD-FHD models.
The non-isothermal Hartmann flow has been chosen as a benchmark physical problem to study
velocity and temperature distributions for Newtonian fluids and non-Newtonian blood flows in
a planar microfluidic channel. In addition to this, the numerical behaviour of an incompressible
and non-isothermal non-Newtonian blood flow has been investigated from computational
aspects when a dipole-like rotational magnetic field generated by infinite conducting wires. The
numerical results are compared to available computational data taken from literature
The computational complexity of traditional Lattice-Boltzmann methods for incompressible fluids
It is well-known that in fluid dynamics an alternative to customary direct
solution methods (based on the discretization of the fluid fields) is provided
by so-called \emph{particle simulation methods}. Particle simulation methods
rely typically on appropriate \emph{kinetic models} for the fluid equations
which permit the evaluation of the fluid fields in terms of suitable
expectation values (or \emph{momenta}) of the kinetic distribution function
being respectively and\textbf{\}
the position an velocity of a test particle with probability density
. These kinetic models can be continuous or discrete in
phase space, yielding respectively \emph{continuous} or \emph{discrete kinetic
models} for the fluids. However, also particle simulation methods may be biased
by an undesirable computational complexity. In particular, a fundamental issue
is to estimate the algorithmic complexity of numerical simulations based on
traditional LBM's (Lattice-Boltzmann methods; for review see Succi, 2001
\cite{Succi}). These methods, based on a discrete kinetic approach, represent
currently an interesting alternative to direct solution methods. Here we intend
to prove that for incompressible fluids fluids LBM's may present a high
complexity. The goal of the investigation is to present a detailed account of
the origin of the various complexity sources appearing in customary LBM's. The
result is relevant to establish possible strategies for improving the numerical
efficiency of existing numerical methods.Comment: Contributed paper at RGD26 (Kyoto, Japan, July 2008
A matrix-free high-order discontinuous Galerkin compressible Navier-Stokes solver: A performance comparison of compressible and incompressible formulations for turbulent incompressible flows
Both compressible and incompressible Navier-Stokes solvers can be used and
are used to solve incompressible turbulent flow problems. In the compressible
case, the Mach number is then considered as a solver parameter that is set to a
small value, , in order to mimic incompressible flows.
This strategy is widely used for high-order discontinuous Galerkin
discretizations of the compressible Navier-Stokes equations. The present work
raises the question regarding the computational efficiency of compressible DG
solvers as compared to a genuinely incompressible formulation. Our
contributions to the state-of-the-art are twofold: Firstly, we present a
high-performance discontinuous Galerkin solver for the compressible
Navier-Stokes equations based on a highly efficient matrix-free implementation
that targets modern cache-based multicore architectures. The performance
results presented in this work focus on the node-level performance and our
results suggest that there is great potential for further performance
improvements for current state-of-the-art discontinuous Galerkin
implementations of the compressible Navier-Stokes equations. Secondly, this
compressible Navier-Stokes solver is put into perspective by comparing it to an
incompressible DG solver that uses the same matrix-free implementation. We
discuss algorithmic differences between both solution strategies and present an
in-depth numerical investigation of the performance. The considered benchmark
test cases are the three-dimensional Taylor-Green vortex problem as a
representative of transitional flows and the turbulent channel flow problem as
a representative of wall-bounded turbulent flows
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