@article{Yang2025, 
author = {Huanhuan Yang and Yanqun Jiang and Qinghong Tang},
title = {Two classes of improved fifth-order weighted compact nonlinear schemes for compressible Euler equations},
year = {2025},
journal = {Electronic Research Archive},
volume = {33},
number = {6},
pages = {3834-3856},
keywords = {Euler equations, WCNS-ZNM scheme, WCNS-P scheme, monotone polynomial interpolation, fifth-order accuracy},
url = {https://www.sciopen.com/article/10.3934/era.2025170},
doi = {10.3934/era.2025170},
abstract = {Two enhanced fifth-order weighted compact nonlinear schemes (WCNSs), namely the WCNS scheme with the modified ZN-type weights (WCNS-ZNM) and the perturbed WCNS scheme (WCNS-P), were proposed for compressible Euler equations. The WCNS-ZNM scheme incorporates an enhanced WENO-ZN-type nonlinear interpolation technique to obtain unknown flow values at cell edges. The WCNS-P scheme introduces perturbation terms containing a free parameter into the linear interpolations, effectively reducing numerical errors in smooth regions. A monotone polynomial interpolation approach was designed to enhance numerical stability by filtering out non-smooth regions and realizing the automatic switching between the WCNS-P and WCNS-ZNM schemes in smooth and non-smooth regions. Numerical results exhibit better accuracy and performance in resolving small-scale structures and shock waves, compared to the WCNS scheme with the WENO-Z and WENO-ZN weights.}
}