Lisa Lechner

•  Wasilij Barsukow, Janina Kern, Christian Klingenberg, Lisa Lechner: "Analysis of the multi-dimensional semi-discrete Active Flux method using the Fourier transform", submitted (2024)  view PDF

Many fluid mechanical problems can be described using hyperbolic systems of conservation laws, such as the Euler equations. The numerical solution of these conservation laws often involves the use of Finite Volume or Discontinuous Galerkin methods. The Active Flux method combines both schemes using a continuous solution reconstruction in the considered domain. My work deals with the further development of a generalized Active Flux scheme. In particular, this scheme allows to solve conservation laws in multiple dimensions with arbitrarily high order. It is expected that this numerical method exhibits many structure preserving properties (e.g. preserving positivity, high fidelity for vortices, low Mach number compliance for the compressible Euler equations).