Oberseminar Mathematische Strömungsmechanik

Consider a high-order scheme for solving hyperbolic conservation laws in semi-discret form. For the time inte-gration the method of lines with a Runge-Kutta method is used. This results in rather restrictive time step. Oneway to overcome this problem is the use of a fully-discretspace-timeDiscontinuous Galerkin method, where thediscretisation of the temporal derivative is done in a similar way as the discretisation of the spatial derivativeof the flux. In order to ensure entropy stability of such a scheme, the discretisation of the volume integral ischanged by a flux derivative projection approach. Additionally entropy conserving and entropy stable temporalstates and spatial fluxes are introduced. Numerical tests show that the derived entropy stable space-time DGmethod maintains the high order of a semi-discret method, it satisfies entropy stability and therefore it is stablefor a wider range of problems.

This is joint work among others with Gregor Gassner and Gero Schnücke.