A Robust Wave Speed Damper for Enhanced WENO-JS Scheme

The Weighted Essentially Non-Oscillatory (WENO) Scheme has a wide range of successful applications, due to the high-order accuracy and essentially non-oscillatory. The 5th order reconstruction of WENO scheme for fluxes or conserved variables tremendously decreases adverse effects of numerical dissipation and has been proposed here. However, the high order is prone to numerically induced symmetry breaking which brings non-physical problematic Ref. [1]., which the symmetry-breaking is relates to vanishing numerical viscosity. In this paper, a robust wave speed damper denoted as ζ, will be introduced by the authors and applied to WENO-JS Ref. [2] to solve hyperbolic partial differential equations named WENO-JSD. The ζ is computed as the ratio of the maximum local acoustic impedance to the average density across the computational domain. The wave speed damper represents the average wave speed when the acoustic wave passes through a discontinuity. This innovative approach outperforms traditional methods reliant on the maximum wave speed for the time-dependent maximum wave speed (λ) in Lax-Friedrichs flux estimations. Remarkably, the proposed technique achieves a significant 7% reduction in errors compared to the λ-based approach when handling critical density discontinuities encountered in the one-dimensional Sod shock tube problem. Furthermore, comprehensive analyses encompassing five diverse configurations of two-dimensional Riemann problems validate the efficacy of ζ. Utilizing ζ noteworthy helps the unsymmetric due to vanishing numerical viscosity and retains necessary accuracy of numerical solutions.