A class of high resolution difference schemes based on non-uniformly cell averaged-solution reconstruction

Based on non-uniformly cell averaged-solution reconstruction,a class of high-order accuracy and high resolution conservative difference schemes is obtained for one-dimensional nonlinear hyperbolic conservation laws in this paper.Its idea is as follows.First,the computational interval is divided into pieces of nonoverlapping sub-intervals,and then each sub-interval is further subdivided into small-intervals by using Gauss-Lobatto and GaussChebyshev partitions according to the required accuracy.Cell averaged-solutions from these small-intervals are used to reconstruct solutions at small-interval boundaries.Furthermore the correction is introduced.Second,the approximate Riemann solver is used to compute numerical fluxes at small-intervals boundaries,and a high-order accurate full discretization method is obtained by applying high-order Runge-Kutta TVD time discretization.Moreover,the non-oscillatory property of the scheme is proved.The extension to systems is implemented.Finally,several typical numerical experients are given.The numerical results verify high accuracy and high resolution of the resulting schemes.