A novel WENO formulation with Mach number-based adaptive numerical dissipation

Eduardo H.S. Lima, Elmo S. Ferreira, Rogério G. dos Santos and Sávio S.V. Vianna

Mathematics and Computers in Simulation (MATCOM), 2026, vol. 239, issue C, 1004-1025

Abstract: The intricate dynamics of shock and discontinuity waves in fluid mechanics demand high-resolution numerical methods for accurate portrayal of multiscale features. The Weighted Essentially Non-Oscillatory (WENO) shock-capturing scheme has advanced in efficiency and precision, focusing on discontinuity regions. This paper introduces an innovative modification to WENO-Z+ and WENO-SV formulations, integrating mesh size and local Mach number as critical parameters to enhance capturing high-speed oscillations and shock-waves accurately. Extending from previous WENO variants, our formulation strategically reduces dissipation at shocks by adjusting weights for less-smooth sub-stencils. This integration of mesh size and local Mach number represents a nuanced solution for challenges posed by high-speed oscillations and shock-waves. Simulations on one and two-dimensional adiabatic and inviscid flow equations validate the efficacy of our approach, revealing good performance over established WENO formulations. Our contribution signifies a pivotal advancement, demonstrating good precision in simulating complex fluid dynamics. This integration of mesh size and local Mach number marks a significant leap towards capturing intricate fluid phenomena with utmost accuracy.

Keywords: WENO scheme; Numerical dissipation; Local Mach number (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:239:y:2026:i:c:p:1004-1025

DOI: 10.1016/j.matcom.2025.07.043

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