Minisymposium “Models, Meshes, Estimates”

Organizer: Dr. Alexander Prechtel

(Monday, 02.03.20, 14:25-15:25, lecture hall H12)

Prof. Dr. Nicole Marheineke (University of Trier):
“Model-Simulation-Framework for Fiber Spinning with Evaporation Effects in Airflows”

Dry spinning of fibers can be described by 3d multiphase multiscale flow models. Governing the key effects, like solvent evaporation and fiber-air interactions, rises the computational complexity such that the direct numerical simulation is in general not possible. We present a dimensionally reduced (1d-2d) fiber model and a problem-tailored numerical solution strategy.  For the numerical treatment of the resulting parametric boundary value problem composed of 1d ordinary differential equations and 2d partial differential equations we develop an iterative coupling algorithm. The solution of the advection-diffusion equations is implicitly given in terms of Green’s functions and leads for the surface values to Volterra integral equations of second kind with singular kernel, which can be solved very efficiently by a product integration method. For the ordinary differential equations a suitable collocation-continuation procedure is employed. Compared with the referential solution of a 3d model, the results are very convincing. They provide a good approximation while drastically reducing the computational time. This efficiency enables the two-way coupled simulation of industrial processes with multiple hundred fibers spun simultaneously in airflows.
 

 

Prof. Dr. Vadym Aizinger (University of Bayreuth):
“Climate modeling on the road to Exascale: From Mathematics to code“

Climate modeling is currently one of the key application areas in dire need of qualitative improvement of modeling skill. This improvement must involve all aspects of numerical model: Mathematical representation of relevant physical, chemical, and biological processes, numerical schemes, and the efficient implementation of model code on modern and future high performance platforms.
In this talk, I’ll present a number of current challenges in numerical model development for climate and its main compartments with a special focus on high performance computing and discuss some strategies aiming at meeting these challenges.

(Tuesday, 03.03.20, 14:05-15:05, lecture hall H12)

Prof. Dr. Lutz Angermann (Clausthal University of Technology):
“Energy balance and active Q-factor control in some nonlinear electromagnetic resonance effects”

The talk presents results on the development and some properties of a mathematical model to describe the excitation effects of a nonlinear material by electromagnetic fields, including typical questions such as the existence and uniqueness of a solution, the derivation of energy balances, the evaluation of the resonance quality and the transfer of these properties to numerical models.

 

Prof. Dr. Markus Bause (Helmut-Schmidt University Hamburg):
“Space-Time FEM on (Un-)Fitted Meshes for Flows and Waves”

Evidence suggests that high-order methods may offer a way to significantly improve the numerical elucidation of physics such as flow and elasticity. Often, such problems encounter complex geometries with immersed and moving boundaries. In this contribution, families of variational space-time finite element methods for their numerical approximation are addressed. In particular, higher-order Galerkin–collocation time discretization is focused. Its conceptual basis is the establishment of a direct connection between the Galerkin method and the classical collocation methods, with the perspective of achieving the accuracy of the former with reduced computational costs of the latter. For wave problems, optimal order error estimates are presented. For flow problems with moving boundaries, the space-time finite element discretization is applied within a Nitsche fictitious domain approach with fixed background mesh and cut cells. Preliminary numerical results are presented, challenges and open problems are discussed.

 

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