Abstract: A new fourth-order semi-discrete central-upwind scheme was constructed for hyperbolic system of conservation laws,convection-diffusion equations and shallow water equations.The integration over the Riemann fans by more accurate information about one-sided local speed of wave propagation was augmented.By using the fourth-order CWENO reconstruction,the new scheme has the properties of higher order accuracy and higher resolution for discontinuities.Because the new scheme has less dissipation,which is independe...