Assessment of Gradient-based Reconstruction and Artificial Diffusivity Methods in Simulating High-Speed Compressible Flows

Abstract

The two promising methods for capturing high-speed flows are local artificial diffusivity (LAD) and centralised gradient-based reconstruction (C-GBR), the former being computationally economical and the latter being more robust and stable but expensive. While the LAD approach captures discontinuities by adding artificial fluid transport coefficients, C-GBR employs a wave appropriate discontinuity sensor to obtain cleaner results and utilises the HLLC approximate Riemann solver for computing inviscid fluxes. The efficacy of these schemes is initially demonstrated in single-species 1D and 2D test cases. Moreover, the shock-capturing capability is assessed for 3D supersonic and hypersonic turbulent boundary layers. The accuracy of LAD predictions is comparable to that of C-GBR for the test case of a supersonic turbulent boundary layer. From the stability front, all simulations are found to be stable with the C-GBR scheme, whereas the LAD-based simulations are observed to abruptly diverge for supersonic and hypersonic flows over compression corners with stronger shocks and larger flow separations. From the computational front, the LAD-based schemes are $1.17 - 2.32 \times$ faster than the monotonicity-preserving explicit/implicit C-GBR schemes. A hybrid approach leveraging the strengths of LAD and GBR schemes is proposed as a promising solution for high-speed turbulent flows with strong shock-boundary layer interactions. The efficacy of the hybrid LAD-GBR solver is demonstrated for the compressible triple-point and supersonic compression ramp test cases. For the M2.9, $24^{\circ}$ case, the hybrid solver was stable and achieved a notable $1.67 \times$ speed-up over the C-GBR scheme.