Schmidt, Alfred

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Schmidt, Alfred
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Schmidt, Alfred

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    An automated hierarchical eXtended finite element approach for multiphysics problems involving discontinuities
    (2018-09-18)
    Jahn, Mischa
    ;
    Montalvo-Urquizo, Jonathan
    ;
    Schmidt, Alfred
    ;
    Schmidt, Alfred
    In this thesis, a hierarchical eXtended finite element method for the modeling and numerical simulation of multiphysics problems and its implementation into a framework that uses automated code generation is presented. The approach consists of introducing hierarchically ordered level set functions, motivated by the structure of the considered problem, to decompose a given hold-all domain into several subdomains. The decomposition is guaranteed to be geometrically consistent which means that no overlapping regions or voids can arise. Mathematically, the approach decouples the computational mesh from the physical domains and, thereby, allows for large deformations and topological changes, such as the rise of (new) subdomains. At domain boundaries, quantities, or their gradient, may be modeled discontinuously and eXtended approximation spaces are introduced for the (sharp) representation of such features on the discrete level. The enrichment is realized by Heaviside functions which are defined subject to the hierarchical level set functions and, hence, introduce additional basis functions and coefficients locally at the respective (sub)domain boundary. For imposing interface and boundary conditions, the Nitsche method is used. By design, the developed approach is well suited to be implemented using automated code generation. As a result, the hierarchical eXtended finite element method is implemented as toolbox miXFEMfor the FEniCS framework. Therefore, the core components of FEniCS are significantly extended and new methods (e.g. the subdivision of elements and the assembling of tensors) are added. As the evolution of interfaces is often part of the problem, the framework miXFEMis supplemented by a level set toolbox providing maintaining methods such as reinitialization and volume correction as well as methods for computing a non-material velocity field. The method and its implementation is validated against several examples and then used for the modeling and simulation of different real-world applications in 2d and 3d. Since this thesis is motivated by several research projects where melting and solidification processes are of interest, we focus on these kind of problems and present results for a thermal upsetting process and different welding processes. However, due to the generality and flexibility of the developed framework, it can be used to rapidly implement and simulate problems from different areas such as multiphase flow or other problems with evolving geometries.
    Dissertation
      489  239
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    Modellierung und Simulation von Prozessen mit fest-flüssig Phasenübergang und freiem Kapillarrand
    (2018-02-28)
    Luttmann, Andreas
    ;
    Bänsch, Eberhard
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    Schmidt, Alfred
    ;
    Schmidt, Alfred
    In this thesis, the material and heat transport for manufacturing processes including a partial melting of metallic workpieces is modeled and simulated. The key aspects of the model are the Navier-Stokes equations including a free capillary surface and wetting for the liquid part and, either a two-phase Stefan problem (interface capturing) or the heat equation in combination with a Stefan condition (interface tracking) to consider the energy balance and allow solid-liquid phase transitions. Both approaches lead to different numerical methods based on an ALE finite element discretization, in which the numerical treatment of the triple junction (solid, liquid, surrounding gas) is crucial. In order to benefit from each method's advantages whilst avoiding their disadvantages, a combined method is proposed. As a simpler but less accurate alternative, a stabilized variant of the interface capturing approach is proposed. The simulation results are validated using experimental data.
    Dissertation
      666  605
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    Stefan-Signorini Moving Boundary ProblemArisen From Thermal Plasma Cutting:Mathematical Modelling, Analysis and Numerical Solution
    (2006-07-25)
    Narimanyan, Arsen
    ;
    Hakobyan,Gurgen
    ;
    Schmidt, Alfred
    ;
    Schmidt, Alfred
    There is a wide range of thermal cutting techniquesavailable for the shaping of materials. One example is the plasma cutting. The cutting of the workpiece occurs as a result of melting/vaporizing the material by an extremely hot cylindrical plasma beam which burns and melts its way through the material, leaving a kerf in its wake. The heat transfer from the plasma beam into the material accounts for most of the phenomena encountered subsequently: shrinkage, residual stresses, metallurgical changes, mechanical deformations, chemical modifications, etc.The work is devoted to the development of a proper mathematical model which must involve the different physical phenomena occurring in the workpiece during the thermal cutting. The aim of the model is then to determine the temperature distribution in the workpiece and thegeometry of the cutting front. Mathematically, we model the problem as a coupled system of equations; heat conduction equation with Signorini-type boundary conditions and level-set equation as a result of reformulation of Stefan-type boundary condition. The mathematicalanalysis and numerical simulations of the model are discussed in the framework of variational inequalities and level-set theory.
    Dissertation
      366  388