Solving conservation laws by ADER central Runge-Kutta schemes

We solve hyperbolic systems of conservation laws with a formulation which combinesthe effectiveness of ADER schemes with the efficiency of central Runge-Kuttaschemes on staggered grids. These new schemes are essentially based on WENOreconstruction of point values from cell averages of initial data, central Runge-Kutta schemes for time advancement, riformulation of the conservation laws byADER schemes. The resulting system is solved on a staggered grid, then avoidingto solve generalized Riemann problems. The results are showed for advection andBurger’s equations and for the Euler system. Comparisons with previous schemesshow the high accuracy of this new approach.