Central Runge-Kutta schemes for conservation laws

In this work, a new formulation for central schemes based on staggered grids is proposed. It is based on a novel approach in which first a time discretization is carried out, followed by the space discretization. The schemes obtained in this fashion have a simpler structure than previous central schemes. For high order schemes, this simplification results in higher computational efficiency. In this work, schemes of order 2 to 5 are proposed and tested, although central Runge-Kutta schemes of any order of accuracy can be constructed in principle. The application to systems of equations is carefully studied, comparing algorithms based on a componentwise extension of the scalar scheme with those based on projection along characteristic directions.