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Minisymposium
Next
CASA minisymposium Wednesday September
7, 2011
Theme:
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Two-scale systems:
Modeling and approximation
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Time:
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13.00 - 16:00 hrs
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| Location: |
HG 6.29
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| Speaker
1: |
Dr. Vladimir Chalupecký
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| Time: |
13:00 - 13:45 hrs
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| Title: |
Numerical analysis of a
two-scale model of acid attack on concrete
Concrete corrosion due to sulfuric acid attack is a phenomena occurring
in sewer pipes that can eventually lead to their collapse. It is a
complex process that includes numerous chemical reactions and
interaction with anaerobic bacteria. We consider a semi-linear
reaction-diffusion PDE/ODE system defined on two separate scales. It
describes the evolution of gaseous H_2S and the conversion of concrete
into gypsum at the macro scale throughout the concrete matrix as well
as
the evolution of dissolved H_2S and H_2SO_4 at pore (micro) scale. We
propose and study a semi-discrete numerical scheme based on finite
difference discretization in space. We derive several a priori
estimates that are necessary to show convergence of the scheme. We also
present an experimental order of convergence study and show several
numerical experiments demonstrating the behavior of the system.
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Speaker
2:
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Prof.dr. Hans Kuipers
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| Time: |
13:45 - 14:30 hrs
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| Title: |
Multi-Scale
Modeling of Dense Particle-Laden Flows
Dense gas-particle
flows are encountered in a variety of industrially important processes
for
large scale production of fuels, fertilizers and base chemicals. The
scale-up
of these processes is often problematic, which can be related to the
intrinsic
complexities of these flows which are unfortunately not yet fully
understood
despite significant efforts made in both academic and industrial
research
laboratories. In dense gas-particle flows both (effective)
fluid-particle and
(dissipative) particle-particle interactions need to be accounted for
because
these phenomena to a large extent govern the prevailing flow phenomena,
i.e.
the formation and evolution of heterogeneous structures. These
structures have
significant impact on the quality of the gas-solid contact and as a
direct
consequence thereof strongly affect the performance of the process. Due
to the
inherent complexity of dense gas-particles flows the authors have
adopted a
multi-scale modeling approach in which both fluid-particle and
particle-particle
interactions can be properly accounted for. The idea is essentially
that
fundamental models, taking into account the relevant details of
fluid-particle
(lattice Boltzmann model) and particle-particle (discrete particle
model)
interactions, are used to develop closure laws to feed continuum models
which
can be used to compute the flow structures on a much larger
(industrial) scale.
Our multi-scale approach (see figure below) involves the lattice
Boltzmann
model, the discrete particle model and the continuum model based on the
kinetic
theory of granular flow. In this presentation the multi-scale modeling
strategy
for dense gas-particle flows will be presented together with
illustrative
computational results. In addition, areas which need substantial
further
attention will be highlighted.
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Speaker
3:
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Dr. Eric Lorenz
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Time:
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14:30 - 15:15 hrs
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Title:
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Heterogenous
multiscale simulations of suspension flow
The macroscopically emergent rheology of suspensions is distated by
details of fluid-particle, and particle-particle interactions. For
systems where the typical spatial scale on the particle level is much
smaller than that of macroscopic properties the scales can be split. We
present a heterogeneous multiscale method (HMM) approach to modeling
suspension flow in which at the macroscale the suspension is treated as
a non-Newtonian fluid. The local shear rate and particle volume
fraction are input to a simulation of fully resolved suspension
microdynamics. With the help of these simulations the apparent
viscosity and shear-induced diffusivities can be computed for a given
shear rate and volume fraction, and are then used to complete the
information needed in the constitutional relations on the macroscopic
level. On both levels the lattice-Boltzmann method (LBM) is applied to
model the fluid phase and coupled to a Lagrangian model for the
advection-diffusion of the solid phase. Down- and upward mapping of
viscosity and diffusivity related quantities will be discussed as well
as information exchanged between the phases on both scales. Temporal
scale splitting between viscous and diffusive dynamics has also been
exploited to accelerate the macrosopic equilibration dynamics.
Additionally, Galileian and rotational symmetries allows to make very
efficient use of a database where the results of previous simulations
can be stored, again reducing the computational effort by factors of
several orders of magnitude.
The HMM suspension model is applied to the simulation of a
2-dimensional flow through a straight channel of macroscopic width. The
equilibration dynamics of flow and volume fraction profiles and
equilibrium profiles of volume fraction, diffusivity, velocity, shear
rate, and viscosity are discused. We show that the proposed HMM mode
not only reproduces experimental findings for low Reynolds numbers but
also predicts additional dependencies introduced by shear-thickening
effects not covered by existing macrosopic suspension flow models.
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Speaker 4:
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Dr. Varvara Kouztnetsova
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Time:
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15:15 - 16:00 hrs
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Title:
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Multi-scale computational
homogenization for non-linear heterogeneous solids
This talk will present a computational homogenization strategy, which
provides a rigorous computational approach to multi-scale modelling of
heterogeneous materials with accurate account for microstructural
characteristics and microstrucural evolution. When using this
micro-macro strategy there is no neccesity to define homogenized
macroscopic constitutive equations, which in case of large deformations
and complex, non-linear microstructures, would generally be a hardly
feasible task. Instead, the constitutive behaviour at a macroscopic
integration point is determined by properly averaging the response of
the deforming microstructure. This enables a straightforward
application of the method to geometrically and physically non-linear
problems, making it a particularly valuable tool for the modelling of
evolving non-linear heteregeneous microstructures under complex
macroscopic loading paths.
In this talk, first the main concepts and the state of the art in the
computational homogenization will be summarized and illustrated on some
representative examples. Some recent extensions of the computational
homogenization scheme will be outlined, i.e. towards second gradient
continuum, shells, heat conduction and thermo-mechanical problems and
localization and damage. Finally, several open issues will be
discussed, primarily related to the violation of the separation of the
spatial and temporal time scales.
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Abstracts of
previous minisymposia
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Inquiries: Marèse Wolfs
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