Analysis for centered nonoscillatory scheme of third order

Choosing symmetric stencils, a centered nonoscillatory scheme of third order scheme (Cn3) constructs a formula which achieves third-order accuracy. A modification of the original estimates, in the reconstruction procedure, was undertaken by employing a monotonicity region as well as an accuracy one. After the very modification, the Cn3 scheme not only obtained nonoscillatory results near discontinuities but also achieved high-accuracy calculation in smooth regions. By using several typical one- and two-dimensional test cases, Cn3 scheme was compared with the weighted essentially non-oscillatory (WENO) schemes of third and fifth order. The properties of capturing discontinuities, stability/robustness and numerical dissipation were significantly considered. The results of the numerical experiments confirm that Cn3 scheme has the ability to suppress spurious numerical oscillations near shocks and contact discontinuities when sharply capturing them, which indicates its characteristics of stability and accuracy, and has low dissipation in smooth region at the same time. Cn3 scheme is worth of further study and application.