A hybrid MPWENO scheme with enhanced accuracy and robustness for the compressible Euler equations

In this study, we develop a hybrid high-order monotonicity-preserving Weighted Essentially Non-Oscillatory (MPWENO) finite difference discretization for the compressible Euler equations. The key innovation of this scheme lies in optimizing the numerical flux through the mixed smooth indicator to reduce the numerical oscillations caused by scheme conversion, and adjusting the reference value to modify the MP limiter, thereby enabling the scheme to achieve the required numerical accuracy while maintaining monotonicity. The novelty of this work lies in systematically adjusting the numerical fluxes by using the mixed smooth indicator to distinguish between discontinuities and extrema and improving the accuracy of the reference value to change the MP limiter, which is different from other MP schemes. The proposed method improves the accuracy at the extreme points, exhibits outstanding robustness and excellent resolution, making it particularly suitable for solving complex problems in compressible Euler equations. Moreover, it is easy to implement and applicable to multi-dimensional problems, with significant practical advantages. Numerical results show that this method has high accuracy, strong robustness, and high resolution. These findings highlight the effectiveness and reliability of this method in handling complex compressible flow simulations.