High Order Accurate TVD Difference Scheme with Applications
Zheng Huasheng(1,2),Zhao Ning(1)
(1 Department of Aerodynamics ,Nanjing University of Aeronautics and Astron autics, Nanjing 210016 ,China)
(2 Department of Information and computational science, Nanchang Institute of Aeronautical Technology, Nanchang 330034 ,China)

Abstract: A class of conservative TVD (Total Variation Diminishing) difference schemes with high order accuracy and resolution, is presented for 1D no nlinear hyperbolic conservation laws. The computational interval is divided into pieces of nonoverlapping sub-intervals, and then each is further subdivided into identically small intervals according to the required accuracy. Cell averaged state variables from these small intervals are used to reconstruct a high order polynomial approximation in the small interval boundaries. Furthermore the correction is introduced to prevent oscillations near discontinuities from the high-order approximation. The approximate Riemann solver is used to compute numerical fluxs on small interval boundaries, and a high-order fully discretization method is obtained by applying high-order Runge-Kutta TVD time discretization . The new scheme enables to accelerate the computation with a higher accuracy and resolution.
Keywords: hyperbolic conservation laws, high order accuracy,TVD difference scheme, Euler equations.