An improved monotonicity-preserving WENO scheme for the Euler equations

Abstract

This paper introduces an innovative fifth-order monotonicity-preserving (MP) scheme that not only achieves remarkable resolution but also preserves monotonicity by skilfully integrating the strengths of the MP and weighted essentially non-oscillatory (WENO) schemes. A novel MP limiter that accommodates a broader range of numerical solutions is proposed, along with several innovative optimization and hybrid techniques designed to enhance the MP scheme’s resolution and robustness. In the context of efficient filtering, the hybrid limiter incorporates a flexible selection process. The proposed scheme switches between the MP5 and WENO5 methods depending on whether the interface values fall within the parameters of the MP limiter. Therefore, the final interface values are derived either from the MP5 scheme or through rigorous post-processing of the WENO5 method and further an optimization procedure by a convex combination technique. This approach maintains both consistency and accuracy in data processing, thereby ensuring more reliable and trustworthy outcomes. The results of one- and two-dimensional numerical experiments indicate that the new scheme outperforms WENO-JS/Z, TENO, MP-R, and MPWENO, delivering superior resolution and exceptional robustness.