Third Order Accurate Difference Scheme of Flux Splitting Based on Averaged Inverse Mapping

Based on the flux splitting and upwind properties,numerical derivative of flux is proposed by introducing averaged inverse mapping. A new third order accurate non-oscillatory flux splitting difference scheme for the one dimensional equation of hyperbolic conservation laws is obtained by using the third order Runge-Kutta TVD time discretization. Finally,several typical numerical examples are given to verify the simplify form and high-resolution of the scheme.