Third-order semi-discrete central-upwind scheme for hyperbolic conservation laws

A third-order semi-discrete central-upwind scheme for one-dimensional system of conservation laws was presented. The scheme is extended to two-dimensional hyperbolic conservation law by the dimension-by-dimension approach. The presented scheme is based on the one-sided local speed of wave propagation. In order to guarantee the accuracy of spatial discretizaiton, a third-order reconstruction is introduced in this paper. The time integration is implemented by using the third-order TVD Runge-Kutta method. The resulting scheme retains the main advantage of the central-schemes simplicity, namely no Riemann solvers are involved and hence characteristic decompositions can be avoided. A variety of numerical experiments in both one and two dimensions are computed. The results show the high accuracy and high resolution of the scheme.