@phdthesis{GallegoValencia2017,
  author    = {Gallego Valencia, Juan Pablo},
  title     = {On Runge-Kutta discontinuous Galerkin methods for compressible Euler equations and the ideal magneto-hydrodynamical model},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-148874},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2017},
  abstract  = {An explicit Runge-Kutta discontinuous Galerkin (RKDG) method is used to device numerical schemes for both the compressible Euler equations of gas dynamics and the ideal magneto- hydrodynamical (MHD) model. These systems of conservation laws are known to have discontinuous solutions. Discontinuities are the source of spurious oscillations in the solution profile of the numerical approximation, when a high order accurate numerical method is used. Different techniques are reviewed in order to control spurious oscillations. A shock detection technique is shown to be useful in order to determine the regions where the spurious oscillations appear such that a Limiter can be used to eliminate these numeric artifacts. To guarantee the positivity of specific variables like the density and the pressure, a positivity preserving limiter is used. Furthermore, a numerical flux, proven to preserve the entropy stability of the semi-discrete DG scheme for the MHD system is used. Finally, the numerical schemes are implemented using the deal.II C++ libraries in the dflo code. The solution of common test cases show the capability of the method.},
  subject      = {Eulersche Differentialgleichung},
  language  = {en}
}