Assessment of AUSM-family flux schemes for axisymmetric flows: Unique numerical challenges and performance trade-offs from transonic to supersonic regimes

Axisymmetric flows present unique numerical challenges absent in planar configurations, with bow shocks positioned closer to bodies, compressing stabilizing subsonic layers and promoting carbuncle instabilities. This study conducts the first systematic evaluation of three AUSM-family schemes (AUSM[Formula: see text]UP, SLAU, AUSM[Formula: see text]M) across inviscid and viscous axisymmetric flows spanning transonic to supersonic regimes. Four benchmarks are examined: supersonic sphere ([Formula: see text]), convergent–divergent nozzle, mixed-compression inlet ([Formula: see text]) and transonic bump ([Formula: see text]). AUSM[Formula: see text]M emerges superior for high-speed axisymmetric applications, uniquely suppressing carbuncle instability on the sphere while achieving 65.8% improvement in post-shock Mach accuracy and 12% shock stand-off error vs AUSM[Formula: see text]UP’s 28.5%. While AUSM[Formula: see text]M incurs a higher computational cost in simpler flows (requiring 54% more CPU time for the sphere case), this expense is justified by its superior capability to suppress carbuncle instabilities and ensure numerical robustness, a trade-off that becomes advantageous in complex configurations where it achieves faster convergence. For the complex inlet, AUSM[Formula: see text]M converges 21.3% faster with optimal total-pressure recovery (3.7% error). It captures shock-induced separation most accurately, predicting separation length within 2.75% on the bump. Conversely, AUSM[Formula: see text]UP exhibits severe shock instabilities, while SLAU consistently fails to resolve strong shocks despite excellent low-Mach performance. Results establish AUSM[Formula: see text]M as the preferred scheme for axisymmetric simulations where shock resolution and numerical stability are paramount.