66 / 2019-09-27 17:46:11

On the propagation and shock-capturing error analyses of weighted compact nonlinear schemes

weighted compact nonlinear schemes,shock-capturing,propagation error

Weighted compact nonlinear schemes (WCNSs) is a popular family of high-order schemes that have been undergoing considerable development in recent years. A number of WCNSs of different forms and order of accuracies have been successfully constructed herein. In the proposed work, we go beyond the case-to-case analysis, and assess the performance of several classical WCNSs on propagation properties of smooth solutions, and the localized shock-capturing properties, by using a general but standardized framework. Moreover, the propagation and shock-capturing errors are quantitatively evaluated. Consistent with expectations, the numerical dispersion and diffusion errors associated with the propagation of disturbances are strongly influenced by the order of accuracies (Fig. 1). It has also been found that although all schemes exhibit expected designed high order of accuracy for smooth solutions, they degrade down to first-order downstream of shocks. What is more, as shown in Fig.2, significant different behaviors at shock are quantitatively determined. The finds in this work can be used as guidelines for the development of new WCNSs with improved performances.