Filters

2010 - 20129

More filters

20199
Reset filters

Settings

search.filters.applied.f.access: openAccess × Author: Dreyer, Wolfgang × End date: 2012 × Start date: 2010 × DDC: 510 × Has files: Yes ×

Search Results

Now showing 1 - 9 of 9
  • Thumbnail Image
    Item
    A diffuse interface model for quasi-incrompressible flows : sharp interface limits and numerics
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2012) Aki, Gonca; Daube, Johannes; Dreyer, Wolfgang; Giesselmann, Jan; Kränkel, Mirko; Kraus, Christiane
    In this contribution, we investigate a diffuse interface model for quasi–incompressible flows. We determine corresponding sharp interface limits of two different scalings. The sharp interface limit is deduced by matched asymptotic expansions of the fields in powers of the interface. In particular, we study solutions of the derived system of inner equations and discuss the results within the general setting of jump conditions for sharp interface models. Furthermore, we treat, as a subproblem, the convective Cahn–Hilliard equation numerically by a Local Discontinuous Galerkin scheme.
  • Thumbnail Image
    Item
    Asymptotic analysis for Korteweg models
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2010) Dreyer, Wolfgang; Giesselmann, Jan; Kraus, Christiane; Rohde, Christiane
    This paper deals with a sharp interface limit of the isothermal Navier-Stokes-Korteweg system. The sharp interface limit is performed by matched asymptotic expansions of the fields in powers of the interface width. These expansions are considered in the interfacial region (inner expansions) and in the bulk (outer expansion) and are matched order by order. Particularly we consider the first orders of the corresponding inner equations obtained by a change of coordinates in an interfacial layer. For a specific scaling we establish solvability criteria for these inner equations and recover the results within the general setting of jump conditions for sharp interface models.
  • Thumbnail Image
    Item
    Exact solutions to the Riemann problem for compressible isothermal Euler equations for two phase flows with and without phase transition
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2011) Dreyer, Wolfgang; Hantke, Maren; Warnecke, Gerald
    We consider the isothermal Euler equations with phase transition between a liquid and a vapor phase. The mass transfer is modeled by a kinetic relation. We prove existence and uniqueness results. Further, we construct the exact solution for Riemann problems. We derive analogous results for the cases of initially one phase with resulting condensation by compression or evaporation by expansion. Further we present numerical results for these cases. We compare the results to similar problems without phase transition.
  • Thumbnail Image
    Item
    Mathematical modeling of Czochralski type growth processes for semiconductor bulk single crystals
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2012) Dreyer, Wolfgang; Druet, Pierre-Étienne; Klein, Olaf; Sprekels, Jürgen
    This paper deals with the mathematical modeling and simulation of crystal growth processes by the so-called Czochralski method and related methods, which are important industrial processes to grow large bulk single crystals of semiconductor materials such as, e.,g., gallium arsenide (GaAs) or silicon (Si) from the melt. In particular, we investigate a recently developed technology in which traveling magnetic fields are applied in order to control the behavior of the turbulent melt flow. Since numerous different physical effects like electromagnetic fields, turbulent melt flows, high temperatures, heat transfer via radiation, etc., play an important role in the process, the corresponding mathematical model leads to an extremely difficult system of initial-boundary value problems for nonlinearly coupled partial differential equations ...
  • Thumbnail Image
    Item
    On balance laws for mixture theories of disperse vapor bubbles in liquid with phase change
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2012) Dreyer, Wolfgang; Hantke, Maren; Warnecke, Gerald
    We study averaging methods for the derivation of mixture equations for disperse vapor bubbles in liquids. The carrier liquid is modeled as a continuum, whereas simplified assumptions are made for the disperse bubble phase. An approach due to Petrov and Voinov is extended to derive mixture equations for the case that there is a phase transition between the carrier liquid and the vapor bubbles in water. We end up with a system of balance laws for a multi-phase mixture, which is completely in divergence form. Additional non-differential source terms describe the exchange of mass, momentum and energy between the phases. The sources depend explicitly on evolution laws for the total mass, the radius and the temperature of single bubbles. These evolution laws are derived in a prior article and are used to close the system. Finally numerical examples are presented.
  • Thumbnail Image
    Item
    Overcoming the shortcomings of the Nernst-Planck model
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2012) Dreyer, Wolfgang; Guhlke, Clemens; Müller, Rüdiger
    This is a study on electrolytes that takes a thermodynamically consistent coupling between mechanics and diffusion into account. It removes some inherent deficiencies of the popular Nernst-Planck model. A boundary problem for equilibrium processes is used to illustrate the new features of our model.
  • Thumbnail Image
    Item
    Blow-up versus boundedness in a nonlocal and nonlinear Fokker-Planck equation
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2011) Dreyer, Wolfgang; Huth, Robert; Mielke, Alexander; Rehberg, Joachim; Winkler, Michael
    Literaturverz.
  • Thumbnail Image
    Item
    A quasi-incompressible diffuse interface model with phase transition
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2012) Aki, Gonca; Dreyer, Wolfgang; Giesselmann, Jan; Kraus, Christine
    This work introduces a new thermodynamically consistent diffuse model for two-component flows of incompressible fluids. For the introduced diffuse interface model, we investigate physically admissible sharp interface limits by matched asymptotic techniques. To this end, we consider two scaling regimes where in one case we recover the Euler equations and in the other case the Navier-Stokes equations in the bulk phases equipped with admissible interfacial conditions. For the Navier-Stokes regime, we further assume the densities of the fluids are close to each other in the sense of a small parameter which is related to the interfacial thickness of the diffuse model.
  • Thumbnail Image
    Item
    Hysteresis and phase transition in many-particle storage systems
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2010) Dreyer, Wolfgang; Guhlke, Clemens; Herrmann, Michael
    We study the behavior of systems consisting of ensembles of interconnected storage particles. Our examples concern the storage of lithium in many-particle electrodes of rechargeable lithium-ion batteries and the storage of air in a system of interconnected rubber balloons. We are particularly interested in those storage systems whose constituents exhibit non-monotone material behavior leading to transitions between two coexisting phases and to hysteresis. In the current study we consider the case that the time to approach equilibrium of a single storage particle is much smaller than the time for full charging of the ensemble. In this regime the evolution of the probability to find a particle of the ensemble in a certain state, may be described by a nonlocal conservation law of Fokker-Planck type. Two constant parameter control whether the ensemble transits the 2-phase region along a Maxwell line or along a hysteresis path or if the ensemble shows the same non-monotone behavior as its constituents.