Assessment of high-order interpolation-based weighted essentially non-oscillatory schemes for compressible Taylor–Green vortex flows

The coexistence and interaction of shock waves and turbulence occur in various applications, such as inertial confinement fusion, scramjet propulsion, and supernova explosions. The supersonic Taylor–Green vortex (TGV) flow is a benchmark example for studying shock/turbulence interaction problems. In this paper, the performance of the interpolation-based weighted essentially non-oscillatory (WENO) schemes for compressible TGV simulation was evaluated, rather than the existing reconstruction-based approach. First, based on the popular unequal-sized WENO (US-WENO) scheme, we developed an interpolation-based US-WENO scheme for simulating three-dimensional inviscid/viscous TGV problems over the Mach number range of 0.1–2.5. Second, a discontinuous sensor based on extremum properties (EPs) of the polynomial was designed, and a corresponding hybrid interpolation-based US-WENO scheme was developed. This EP-based sensor does not contain empirical parameters and can simulate the supersonic TGV problems well while significantly improving the computational efficiency of the original US-WENO scheme. Numerical experiments show that the interpolation-based WENO scheme has smaller numerical dissipation and better performance for compressible TGV problems than the reconstruction-based WENO scheme. However, its computational cost is slightly higher, while the hybrid US-WENO scheme can perform better in terms of both computational accuracy and efficiency.