Entropy based flux limiting scheme for conservation laws

The construction of high-resolution shock-capturing schemes is vital inproducing highly accurate gravitational waveforms from neutron star binaries.The entropy based flux limiting (EFL) scheme is able to perform fast convergingbinary neutron star merger simulations reaching up to fourth-order convergencein the gravitational waveform phase. Here, we extend the applicability of theEFL method beyond special/general relativistic hydrodynamics to scalarconservation laws and show how to treat systems without a thermodynamicentropy. This is an indication that the method has universal applicability toany system of partial differential equations that can be written inconservation form. We also present some further very challengingspecial/general relativistic hydrodynamics applications of the EFL method anduse it to construct eccentricity reduced initial data for a specific neutronstar binary and show up to optimal fifth-order convergence in the gravitationalwaveform phase for this simulation.