## Doktorandenseminar des WIAS

# Numerische Mathematik und Wissenschaftliches Rechnen

Forschungsgruppe

2017
(2016,
2015,
2014,
2013,
2012,
2011,
2010,
2009,
2008,
2007,
2006,
2005,
2004,
2003,
2002)
## Seminar Numerische Mathematik / Numerical mathematics seminars

aktuelles Programm / current program

_{FG3 intern}

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Donnerstag, 03. 05. 2018, 14:00 Uhr (ESH)
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Dr. H. Stephan(WIAS Berlin)

One million perrin pseudo primes including a few giantsPseudoprimes are integers that are no primes but behave like them in some sense. Suppose we have a theorem like the following: If n is a prime, then statement A(n) holds. In general, the opposite is not true: It may be that A(n) holds, but n is a composite number, a so-called pseudo prime with respect to statement A. Pseudoprimes are interesting if they are very rare, as for instance Perrin's pseudoprimes, the smallest of which is 271441. The talk introduces pseudoprimes which are based on recurrent sequences. In addition, some new numerical results on Perrin's pseudoprimes and a fast algorithm for their calculation are presented.

und 15:00 Uhr

L. Feierabend(Universität Duisburg-Essen)

Model development for flowing slurry electrodes in zinc-air batteriesSlurry or suspension electrodes are gaining a renewed interest for large-scale energy storage technologies due to potentially higher energy densities compared to redox flow batteries [1]. A suspension electrode typically consists of a liquid electrolyte and a solid material, which is chemically active and electrically conducting. For the investigated zinc-air flow batteries employing a suspension electrode, microscopic zinc particles are suspended in an aqueous potassium hydroxide electrolyte [2, 3]. Sedimentation of the metallic zinc is minimized by adding a gelling agent to the electrolyte. The gelling agent and the high particle loading lead to a pseudo-plastic rheological behavior. When the flowable suspension electrode is pumped through the channels of the zinc-air fuel cell setup, the dynamic percolation network within the suspension dictates the active electrode surface area and the maximum discharge power density. Therefore, it is desirable to investigate the influence of the local flow conditions on the particle percolation and consequently the electrochemical performance of the battery cell with adequate simulation methods. In the developed three-dimensional numerical model for the flowing suspension electrode, the complex, non-Newtonian two-phase flow is approximated by a coupling of an Eulerian continuum description for the electrolyte and a discrete, Lagrangian particle description for the motion and interaction of the microscopic particles. The partial differential equations for momentum, species, charge and energy are discretized by the finite volume method and implemented in the OpenFOAM library [4]. The particle motion including multiple simultaneous particle contacts is described with the discrete element method using the LIGGGHTS library [5]. Coupling between the particle and fluid phase is realized with the CFD-DEM method using the CFDEM library [5], where an empirical description accounts for the momentum exchange between the non-Newtonian fluid and the densely distributed particle assemblies. Due to relatively high particle concentrations, the volume displacement by the particles is considered in the electrolyte continuum model. A half-cell model for the anode part of the zinc-air flow battery is implemented, which accounts for the flow characteristics via the described CFD-DEM coupling method. Simultaneously, the charge and species transport is considered according to the classic porous electrode theory by Newman [6] adapted with newer formulations for concentrated electrolytes [7]. In contrast to electrodes with a static porous matrix, the heterogeneous local porosities change temporally depending on the evolving particle distributions. Additionally, the active electrode surface area in each finite volume is dependent on the percolation network from the considered local point to the current collector surface. To estimate the basic parameters for the charge transfer and species transport, a flat-plate electrode with a flowing electrolyte without particles is investigated. In this rather simple reference case, discontinuities of the current density close to the electrode-electrolyte-interface could be observed, which should be inherently excluded due to the model formulations. These inconsistencies will be discussed in detail. Funding by the Federal Ministry for Economic Affairs and Energy (BMWi) of the project “ZnPLUS -Wiederaufladbare Zink-Luft-Batterien zur Energiespeicherung” and the project “ZnMobil - Mechanisch und elektrisch wiederaufladbare Zink-Luft-Batterie für automobile Anwendungen” is gratefully acknowledged.

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Mittwoch, 18. 04. 2018, 13:30 Uhr (ESH)
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Prof. P. Deuring(Universitè du Littoral ''Côte d'Opale'', Frankreich)

Stabilitäts- und Fehlerschranken einer FE-FV-Diskretisierung von Konvektions-Diffusionsgleichung: exponentielle Abhängigkeit von ParameternWir betrachten eine FE-FV-Methode zur Bestimmung von Näherungslösungen von Konvektions-Diffusionsgleichungen. Bei dieser Methode wird der Diffusionsterm mittels Crouzeix-Raviart-Elementen diskretisiert, während man den Konvektionsterm durch baryzentrische finite Volumen approximiert. Wir gehen der Frage nach, ob sich Stabilitäts- und Fehlerschranken für diese Methode finden lassen, die von keiner Größe exponentiell abhängen, insbesondere nicht vom Kehrwert des Diffusionskoeffizienten.

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Donnerstag, 12. 04. 2018, 14:00 Uhr (ESH)
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Prof. M. J. Neilan(University of Pittsburgh, USA)

Inf-sup stable Stokes pairs on barycentric refinements producing divergence-free approximationsWe construct several stable finite element pairs for the Stokes problem on barycentric refinements in arbitrary dimensions and for any polynomial degree. A key feature of the spaces is that the divergence maps the discrete velocity space onto the discrete pressure space; thus, when applied to models of incompressible flows, the pairs yield divergence-free velocity approximations. The key ingredients to prove these results are local inf-sup stability estimates and a modification of Bernardi-Raugel bubble functions. This is joint work with Johnny Guzman.

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Donnerstag, 01. 03. 2018, 14:00 Uhr (ESH)
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Dr. F. Dassi(Politecnico di Milano, Italien)

Recent advancements of the Virtual Element Method in 3DThe Virtual Element Method is a novel way to discretize a partial differential equation. It avoids the explicit integration of shape functions and introduces an innovative construction of the stiffness matrix so that it acquires very interesting properties and advantages. One among them is the possibility to apply the VEM to general polygonal/polyhedral domain decomposition, also characterized by non-conforming and non-convex elements.

In this talk we focus on the definition/construction of the Virtual Element functional spaces in three dimensions and how apply this new strategy to set a standard Laplacian problem in 3D.

Finally we test the method to show its robustness with respect to element distortion and the polynomial approximation degree $k$. Then, we move to more involved cases: convection-diffusion-reaction problems with variable coefficients and magnetostatic Maxwell equations.

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Donnerstag, 01. 02. 2018, 14:00 Uhr (ESH)
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Dr. E. Sinibaldi(Italian Institute of Technology)

Selected modeling approaches for biomedical applications and biorobotics toolsThe effective deployment of theranostic agents (including drugs), smart?materials?based systems and interfaces to target regions (prospectively) in the human body where to perform the sought actions also requires theoretical models and physical tools. Modeling the delivery and the (remote) actuation/stimulation of the aforementioned agents/systems/interfaces, in particular, permits to compensate for experimental conditions hard to characterize and to better interpret the experimental results, thus paving the way for quantitative therapy design and control. This is complemented by model-based design of related experimental devices, flexible tools able to safely navigate anatomical pathways, and miniaturized effectors. In this talk I will firstly present the solution to an inverse problem, namely to determine the velocity profile in a vessel cross-section starting from the flow-rate, which is relevant to pulsatile biological flows (blood and cerebro-spinal fluid flows), with application, e.g., to magnetic particle targeting. Then I will address numerical models for intrathecal drug-delivery (drug infusion in the cerebro-spinal fluid, also accounting for transport to the spinal cord) and simplified analytical models for intra-tissue drug-delivery (particle transport into porous/poroelastic media, with application to intratumoral thermotherapy). Finally, I will overview model-based approaches for: piezoelectric nanoparticle-mediated cell stimulation; real-scale physical models of the blood-brain barrier; flexible biorobotics probes; miniature (bioinspired) actuators and effectors.

und 15:00 Uhr

L. Blank(WIAS Berlin)

Towards a simple and robust finite element method for the numerical simulation of porous media flowThe topic of this talk is the numerical simulation of flow through porous media based on the Brinkman model as a unified framework that allows the transit between Darcy and Stokes problems. Therefore an unconditionally stable low order finite element approach, which is robust with respect to the physical parameters, is proposed. This approach is based on the combination of stabilized equal order finite elements with a non-symmetric (penalty-free) Nitsche method for the weak imposition of essential boundary conditions. Focusing on the two-dimensional case, optimal a priori error estimates in a mesh-dependent norm, which allows to extend the results also to the Stokes and Darcy limits, are obtained.

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Donnerstag, 18. 01. 2018, 14:00 Uhr (ESH)
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Prof. W. Dreyer(WIAS Berlin)

Modeling of non-Newtonian fluids without material frame indifferenceIn the fifties the modeling of

non-Newtonian fluidsinitiated the search for invariant time derivatives with respect to certain space time transformations. ThenEuclidean Transformationswere selected to establish thePrinciple of Material Frame Indifferenceand moreover, the introduction of N^{th}grade fluids. However, the two concepts lead to serious inconsistencies in both thermodynamic modeling and experimental observations. In 1986 the subject has been resolved in a remarkable paper by I. Müller and K. Wilmanski. In this lecture we show how an appropriate model ofnon-Newtonian fluidsmay be incorporated inContinuum Thermodynamicsas it was laid down by D. Bothe and W. Dreyer.

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Donnerstag, 11. 01. 2018, 14:00 Uhr (ESH)
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Prof. G. Lube(Georg-August-Universität Göttingen)

Why exactly divergence-free H(div)-conforming FEM for transient incompressible flows?Recent results show that one can reconstruct classical inf-sup stable H1-conforming FEM for incompressible flow problems to be pressure-robust. Exactly divergence-free FEM are pressure-robust per construction. In particular, exactly divergence-free H(div)-conforming FEM combine excellent stability and conservation properties with minimal stabilization. We show that the numerical analysis of such methods allows to separate the (static) linear Stokes regime and the nonlinear dynamic regime. Semi-robust error estimates w.r.t. the Reynolds number will be given. In a hybridized form, H(div)-conforming FEM are suitable for large scale computation. Applications of the approach to two- and three-dimensional problems of vortex dynamics will be presented for high Reynolds numbers.

und 15:00 Uhr

Dr. A. Rasheed(Lahore University of Management Sciences, Pakistan)

Influence of magnetic field on dendrites during solidification of binary mixturesA phase field model has been proposed which incorporates convection and magnetic field in an isothermal environment. A numerical scheme is proposed and numerical analysis of model in two-dimensional geometry is performed. The numerical stability and error analysis of this approximation scheme which is based on mixed finite-element method are performed. An application of a nickel-copper binary alloy is considered. Influence of various magnetic fields on the dendrites during the solidification process has been discussed.