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Author: John, Volker Ă— Start date: 2010 Ă— DDC: 510 Ă— Type: Article Ă— WGL Institute: WIAS Ă—

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    Optimal control of buoyancy-driven liquid steel stirring modeled with single-phase Navier–Stokes equations
    (Berlin ; Heidelberg : Springer, 2021) Wilbrandt, Ulrich; Alia, Najib; John, Volker
    Gas stirring is an important process used in secondary metallurgy. It allows to homogenize the temperature and the chemical composition of the liquid steel and to remove inclusions which can be detrimental for the end-product quality. In this process, argon gas is injected from two nozzles at the bottom of the vessel and rises by buoyancy through the liquid steel thereby causing stirring, i.e., a mixing of the bath. The gas flow rates and the positions of the nozzles are two important control parameters in practice. A continuous optimization approach is pursued to find optimal values for these control variables. The effect of the gas appears as a volume force in the single-phase incompressible Navier–Stokes equations. Turbulence is modeled with the Smagorinsky Large Eddy Simulation (LES) model. An objective functional based on the vorticity is used to describe the mixing in the liquid bath. Optimized configurations are compared with a default one whose design is based on a setup from industrial practice.
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    A unified analysis of algebraic flux correction schemes for convection–diffusion equations
    (Berlin ; Heidelberg : Springer, 2018) Barrenechea, Gabriel R.; John, Volker; Knobloch, Petr; Rankin, Richard
    Recent results on the numerical analysis of algebraic flux correction (AFC) finite element schemes for scalar convection–diffusion equations are reviewed and presented in a unified way. A general form of the method is presented using a link between AFC schemes and nonlinear edge-based diffusion schemes. Then, specific versions of the method, that is, different definitions for the flux limiters, are reviewed and their main results stated. Numerical studies compare the different versions of the scheme.