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47:23 Weierstraß-Institut für Angewandte Analysis und Stochastik (WIAS), Technische Informationsbibliothek (TIB) German 2017

"Extreme Fluids" - Some Examples, Challenges and Simulation Techniques for Flow Problems with Complex Rheology

In this talk we discuss numerical simulation techniques for incompressible fluids with complex rheology which means that local flow characteristics may differ significantly by several orders of magnitude, for instance due to non-isothermal behavior and pressure, resp., shear dependent viscosity. Such fluids usually include viscoplastic as well as viscoelastic effects which is typical for yield-stress fluids, granular material as well as polymer melts and kautschuk. Corresponding applications are relevant for polymer processing, but include also viscoplastic lubrication, fracking and macro encapsulation. In this talk, we present special discretization and solver techniques in which case the coupling between the velocity, pressure and additional variables for the stresses, which leads to restrictions for the choice of the FEM approximation spaces, and the (often) hyperbolic nature of the problem are handled with special Finite Element techniques including stabilization methods. The resulting linearized systems inside of outer Newton-like solvers are (special) nonsymmetric saddle point problems which are solved via geometrical multigrid approaches. We illustrate and analyze numerically the presented methodology for well-known benchmark configurations as well as protoypical industrial applications for several nonlinear flow models.
  • Published: 2017
  • Publisher: Weierstraß-Institut für Angewandte Analysis und Stochastik (WIAS), Technische Informationsbibliothek (TIB)
  • Language: German
52:42 Weierstraß-Institut für Angewandte Analysis und Stochastik (WIAS), Technische Informationsbibliothek (TIB) English 2017

Machine learning and applications

Since a few years Machine Learning (ML) has broadened the modeling toolbox for the sciences and industry. The talk will first remind the audience of the main ingredients for applying machine learning. Then various ML applications in the sciences namely Brain Computer Interfaces and Quantum Chemistry will be discussed.
  • Published: 2017
  • Publisher: Weierstraß-Institut für Angewandte Analysis und Stochastik (WIAS), Technische Informationsbibliothek (TIB)
  • Language: English
25:03 Weierstraß-Institut für Angewandte Analysis und Stochastik (WIAS), Technische Informationsbibliothek (TIB) German 2017

Mathematical knowledge management as a route to sustainability in mathematical modeling and simulation

Mathematical modeling and simulation (MMS) has now been established as an essential part of the scientific work in many disciplines. It is common to categorize the involved numerical data and to some extend the corresponding scientific software as research data. Both have their origin in mathematical models. A holistic approach to research data in MMS should cover all three aspects: models, software, and data. Yet it is unclear, whether a suitable management of the mathematical knowledge related to models is possible and how it would look like. In this talk, we outline an approach to address this problem based on a flexiformal representation of the mathematical knowledge in scientific publications and discuss how this can contribute to sustainable research in MMS.
  • Published: 2017
  • Publisher: Weierstraß-Institut für Angewandte Analysis und Stochastik (WIAS), Technische Informationsbibliothek (TIB)
  • Language: German
42:16 Weierstraß-Institut für Angewandte Analysis und Stochastik (WIAS), Technische Informationsbibliothek (TIB) English 2017

An introduction to inverse problems with applications in machine learning

The presentation starts with some motivating examples of Inverse Problems before introducing the general setting. We shortly review the most common regularization approaches (Tikhonov, iteration methods) and sketch some recent developments in sparsity and machine learning. Sparsity refers to additional expert information on the desired reconstruction, namely, that is has a finite expension in some predefined basis or frame. In machine learning we focus on 'multi colored' inverse problems, where part of the application can be formulated by a strict analytical framework but some part of the problem needs to modeled by a data driven approach. Those combined problems can be created by data- driven linear low rank approximations or more general black box models. In particular we review deep learning approaches to inverse problems. Finally, machine learning techniques by themselves are often inverse problems. We highlight basis learning techniques and applications to hyperspectral image analysis.
  • Published: 2017
  • Publisher: Weierstraß-Institut für Angewandte Analysis und Stochastik (WIAS), Technische Informationsbibliothek (TIB)
  • Language: English
19:20 Weierstraß-Institut für Angewandte Analysis und Stochastik (WIAS), Technische Informationsbibliothek (TIB) German 2017

On new developments in the discretization theory for PDEs, possibly relevant for GFD & CFD

In this talk, an overview will be given on some new developments in the field of discretization theory for partial differential equations, which are possibly relevant for applications in CFD & GFD. Among them are: pressure-robust schemes for the incompressible Navier-Stokes equations, physically-consistent discretizations, discretizations on polyhedral meshes
  • Published: 2017
  • Publisher: Weierstraß-Institut für Angewandte Analysis und Stochastik (WIAS), Technische Informationsbibliothek (TIB)
  • Language: German
14:59 Weierstraß-Institut für Angewandte Analysis und Stochastik (WIAS), Technische Informationsbibliothek (TIB) German 2017

Consistent 3D turbulence parametrization in circulation models

We present an extension of the Dynamic Smagorinsky model (DSM) to parameterize the subgrid-scale momentum diffusion in global circulation models (GCM) In contrast to the standard approach, the test filter to determine the Smagorinsky parameter is separated from the resolution scale to exclude potential interactions. In addition, in GCMs the horizontal and vertical scales are usually treated differently due to gravity. While for the turbulent vertical diffusion of horizontal momentum a classical Smagorinsky approach is common, the respective horizontal diffusion in the free atmosphere is usually neglected. We show how to formulate the generalized DSM as subgrid-scale horizontal momentum diffusion to run stably a GCM without hyperdiffusion. Furthermore, the idea of stratified turbulence is applied to find a dynamic approach also for the vertical diffusion. Both improvements allow for a realistic spectrum of kinetic energy (almost) up to the resolution scale.
  • Published: 2017
  • Publisher: Weierstraß-Institut für Angewandte Analysis und Stochastik (WIAS), Technische Informationsbibliothek (TIB)
  • Language: German
13:52 Weierstraß-Institut für Angewandte Analysis und Stochastik (WIAS), Technische Informationsbibliothek (TIB) German 2017

An online coupled Lagrangian particle dispersion model for COSMO

Lagrangian particle dispersion models (LPDM) are a well-known method for modeling exhaust gas distributions and similar problems. Open accessible LPDM's, e.g., the FLEXPART model are designed for meso-scale simulations and work offline coupled with the coarse frequented output data of any numerical weather prediction model. But the central issue there is that high resolution simulations of small scale phenomena need a high frequency input of meteorological data fields to work accuracy, which can directly be provided by an online coupled model system. Based on the COSMO trajectory module the model LAPASI was developed that integrates an online coupled Lagrangian particle transport into the default COSMO version. It supports any kind of simulation that are possible with the COSMO including idealized cases and can handle a couple Million particles with individual start times, start locations and dry depositions velocities. Thus, LAPASI is a useful extension for COSMO and a necessary addition to the previously existing LPDM's.
  • Published: 2017
  • Publisher: Weierstraß-Institut für Angewandte Analysis und Stochastik (WIAS), Technische Informationsbibliothek (TIB)
  • Language: German
25:37 Weierstraß-Institut für Angewandte Analysis und Stochastik (WIAS), Technische Informationsbibliothek (TIB) German 2017

Thermodynamically consistent modeling of fluids

The motion of fluids is restricted by the 2nd Law of Thermodynamics in multiple manner. This lecture uses historical and contemporary issues to illustrate both the general structure and special properties of thermodynamically consistent modeling.
  • Published: 2017
  • Publisher: Weierstraß-Institut für Angewandte Analysis und Stochastik (WIAS), Technische Informationsbibliothek (TIB)
  • Language: German
14:56 Weierstraß-Institut für Angewandte Analysis und Stochastik (WIAS), Technische Informationsbibliothek (TIB) German 2017

Split-explicit methods for low Mach number flows with cut cell discretization

Split-explicit methods are a common integration method in numerical weather prediction. They combine two explicit methods to integrate different parts of the right hand side with different time steps. Common combinations are for the slow part Leap-Frog, Runge-Kutta, or Adams-method and for the fast part a Verlet-type integration method. For Runge-Kutta methods as the slow integrator Wensch et.al give a generalization (MIS-method) and analysed this new method in case of an exact integration of the fast part. When the orography is represented by a cut cell approach the splitting has to respect also the small cell problem. Modifications are described, which represent the fast part by a local linear operator and use a special implicit-explicit method for the integration of this linear differential equation. We will compare our new integrators and known methods for the two-dimensional compressible Euler-equations for examples with different Mach-numbers and grid configurations.
  • Published: 2017
  • Publisher: Weierstraß-Institut für Angewandte Analysis und Stochastik (WIAS), Technische Informationsbibliothek (TIB)
  • Language: German
24:27 Weierstraß-Institut für Angewandte Analysis und Stochastik (WIAS), Technische Informationsbibliothek (TIB) English 2017

On perspectives for common research in the Leibniz MMS network in the field of Computational and Geophysical Fluid Dynamics

Computational Fluid Dynamics (CFD) and Geophysical Fluid Dynamcis (GFD) are common research topics of different Leibniz institutes, where very similar mathematical and physical modelling approaches are used. Therefore, CFD & GFD seem to be obvious candidates for interdisciplinary research in the Leibniz Association. In the talk, an overview is given about the first common MMS research activities in the field of (CFD & GFD), and some perspectives for common research are presented.
  • Published: 2017
  • Publisher: Weierstraß-Institut für Angewandte Analysis und Stochastik (WIAS), Technische Informationsbibliothek (TIB)
  • Language: English
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