Abstract: A high-order,high resolution,conservative TVD difference scheme is presented for one dimensional hyperbolic conservation equations.The basic idea is as follows.Firstly,the computation domain is divided into many non-overlapping subdomains,and then each subdomain is further subdivided into small cells according to the required accuracy; Secondly,by the flow direction,flux splitting is introduced,and high-order approximation in the subdomain are used to compute the positive/negative numerical fluxes at cell boundaries.Furthermore,TVD corrections are considered to prevent oscillations near discontinuities from the high-order interpolation.Moreover,by means of high-order TVD Runge-Kutta time discretization,a high-order fully discretization method is obtained.The extension to one dimensional systems is also carried out.Finally,numerical experiments on one dimensional Euler equations are given,and numerical results are satisfactory.

Key words: hyperbolic conservation laws, flux splitting, TVD difference scheme, high order accuracy, Euler equations