A Class of Second-Order Accurate Difference Schemes Based on Flux Splitting

Combined with second order Runge-Kutta TVD time discretization method,a new class of second order accurate scheme in space and time is obtained to solve the one dimensional hyperbolic conservation law by applying splitting,reconstruction and correction of the numerical fluxes.The extension to systems is carried out by using component-wise manner and characteristic decomposition manner respectively.Finally,some typical numerical experiments are given to verify the validity of the schemes.