@phdthesis{Berberich2021,
  author    = {Berberich, Jonas Philipp},
  title     = {Fluids in Gravitational Fields - Well-Balanced Modifications for Astrophysical Finite-Volume Codes},
  doi       = {10.25972/OPUS-21967},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-219679},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2021},
  abstract  = {Stellar structure can -- in good approximation -- be described as a hydrostatic state, which which arises due to a balance between gravitational force and pressure gradient. Hydrostatic states are static solutions of the full compressible Euler system with gravitational source term, which can be used to model the stellar interior. In order to carry out simulations of dynamical processes occurring in stars, it is vital for the numerical method to accurately maintain the hydrostatic state over a long time period. In this thesis we present different methods to modify astrophysical finite volume codes in order to make them \emph{well-balanced}, preventing them from introducing significant discretization errors close to hydrostatic states. Our well-balanced modifications are constructed so that they can meet the requirements for methods applied in the astrophysical context: They can well-balance arbitrary hydrostatic states with any equation of state that is applied to model thermodynamical relations and they are simple to implement in existing astrophysical finite volume codes. One of our well-balanced modifications follows given solutions exactly and can be applied on any grid geometry. The other methods we introduce, which do no require any a priori knowledge, balance local high order approximations of arbitrary hydrostatic states on a Cartesian grid. All of our modifications allow for high order accuracy of the method. The improved accuracy close to hydrostatic states is verified in various numerical experiments.},
  subject      = {Fluid},
  language  = {en}
}
@phdthesis{Sonder2010,
  author    = {Sonder, Ingo},
  title     = {Non-Newtonian Properties of Magmatic Melts},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-49762},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2010},
  abstract  = {This work presents a new method to measure model independent viscosities of inhomogeneous materials at high temperatures. Many mechanisms driving volcanic eruptions are strongly influenced by the viscous properties of the participating materials. Since an eruption takes place at temperatures at which these materials (predominantly silicate melts) are not completely molten, typically inhomogeneities, like e.g. equilibrium and non-equilibrium crystals, are present in the system. In order to incorporate such inhomogeneities into objective material parameters the viscosity measurement is based on a rotational viscometer in a wide gap Couette setup. The gap size between the two concentric cylinders was designed as large as possible in order to account for the inhomogeneities. The emerging difficulties concerning the model independent data reduction from measured values to viscosities are solved using an appropriate interpolation scheme. The method was applied to a material representative for the majority of volcanic eruptions on earth: a typical continental basaltic rock (Billstein/Rh{\"o}n/Germany). The measured viscosities show a strong shear rate dependency, which surprises, because basaltic melt has been, until now, assumed to behave as a Newtonian fluid. Since a non-Newtonian material shows a very different relaxation behavior in the Couette motion compared to a Newtonian one (which, ultimately, does not show any), and a strong relaxation signal was recorded during viscosity measurements, the equations of Couette motion were investigated. The time dependent stress distribution in a material due to a quasi step-like velocity change at the inner Couette radius (i.e. the spindle) was considered. The results show that a material combining a linear shear modulus and a Newtonian viscosity -- a Maxwell material -- cannot quantify the relaxation behavior. This could be considered as a hint, that the widely used Maxwell relaxation times cannot be applied as a 1:1 mapping from microscopic considerations to macroscopic situations.},
  subject      = {Viskosit{\"a}t},
  language  = {en}
}