A Kind of Difference Schemes Based on Flux Splitting and Least Squares Fitting

Based on the flux splitting with positive and negative fluxes and their least squares fitting,a new kind of second order accurate scheme is obtained for the one dimensional equations of hyperbolic conservation laws according to the flow directions and upwind properties,and applying second order Runge-Kutta TVD time discretization.Furthermore,the extension to systems is straightforward by using component-wise manner.Finally,some typical numerical experiments are given.The numerical results verify the validity of the schemes.