(untitled) (Communications in Computational Physics, 2025)
Most high-order computational fluid dynamics methods for compressible flows are based on the Riemann solver for the flux evaluation and high-order interpolation or reconstruction such as the Weighted Essential Non-Oscillatory (WENO) scheme for spatial accuracy. The advantage of this kind of combination is the easy implementation and the ability to achieve the required spatial accuracy. However, despite the extensive research on high-order spatial reconstruction in the past, solvers coupling high-order space and time schemes have not been systematically evaluated. In this paper, based on the same fifth-order finite volume method (FVM), comparisons of the performance of the same flux solver with different reconstructions and the same reconstruction but different flux solvers are carried out on a structured mesh. For reconstruction, the TENO scheme and classic WENO-Z reconstruction have been chosen as representative methods. Meanwhile, for the flux solver, Lax-Friedrichs (LF) Riemann solver, HLLC solver, and GKS are considered. Through a series of simulated comparison cases, the unique characteristics of GKS and TENO have been demonstrated. Overall, the comparisons suggest that proper spatial and temporal coupling is important for accurate shock and vortex capturing.