A kind of two-dimensional high-order accurate difference schemes based on non-uniformly partition

Extending a class of high resolution difference schemes based on non-uniformly cell averaged-solution reconstruction for one dimensional nonlinear hyperbolic conservation laws to two-dimensional scalar hyperbolic conservation laws,a kind of two dimensional high-order accurate difference schemes is obtained by using dimension-by-dimension method for two-dimensional nonlinear hyperbolic conservation laws in this paper.Moreover,the non-oscillatory property of these schemes is proved.The extension to systems is carried out.Finally,several typical numerical experiments are given.The numerical results show that these schemes have high-order accuracy and high resolution for capturing shock waves.