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Minisymposium

Next CASA minisymposium Wednesday September 7, 2011

Theme:
Two-scale systems: Modeling and approximation
Time:
13.00 - 16:00 hrs
Location: HG 6.29


Speaker 1: Dr. Vladimir Chalupecký
Time: 13:00 - 13:45 hrs
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.


Speaker 2:
Prof.dr. Hans Kuipers
Time: 13:45 - 14:30 hrs
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.



Speaker 3:
Dr. Eric Lorenz
Time:
14:30 - 15:15 hrs
Title:
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.


Speaker 4:
Dr. Varvara Kouztnetsova
Time:
15:15 - 16:00 hrs
Title:
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.
Abstracts of previous minisymposia
Inquiries: Marèse Wolfs
© Centre for Analysis, Scientific Computing and Applications. For questions please refer to the editor.
This page modified: Fri Jul 29 11:05:43 CEST 2011