Towards optimal high-order compact schemes for simulating compressible flows

摘要

Weighted compact nonlinear schemes (WCNS) (Deng and Zhang, 2000) were developed to improve the performance of the compact high-order nonlinear schemes (CNS) by utilizing the weighting technique originally designed for WENO schemes, and excellent shock capturing capability and high resolution are achieved. Numerous articles have been contributing to improving the performance of WCNSs ever since. In this work, the ENO-like stencil selection procedure of Targeted ENO schemes is introduced for interpolating midpoint variables, targeting compact nonlinear schemes which fully abandon the oscillatory stencils crossing discontinuities, and directly apply optimal linear weights when the flow field is smooth, such that the optimal numerical resolution is fully recovered in smooth flow field. Several canonical numerical cases of scalar equations and the Euler equations of gas dynamics are given to examine the performance of the presented method.