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

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

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.

Suggested Citation

  • Lima, Eduardo H.S. & Ferreira, Elmo S. & dos Santos, Rogério G. & Vianna, Sávio S.V., 2026. "A novel WENO formulation with Mach number-based adaptive numerical dissipation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 239(C), pages 1004-1025.
    • Handle: RePEc:eee:matcom:v:239:y:2026:i:c:p:1004-1025
    DOI: 10.1016/j.matcom.2025.07.043
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