Oberseminar Mathematical Fluid Dynamics

The Active Flux (AF) method uses characteristics in order to update point values: given a reconstruction
in space, the new value is found at the foot of the characteristic. For implicit methods, i.e. large CFL numbers,
these characteristics cross distances much larger than one cell over one time step, and their foot is essentially
unavailable. We employ a new reconstruction-in-time technique to obtain stable implicit Active Flux methods of
up to 5th order of accuracy. Numerical results demonstrate the superiority of these methods over implicit Finite
Difference methods and semi-discrete AF methods that are integrated using implicit Runge-Kutta methods.
This is joint work with Raul Borsche (University of Kaiserslautern).