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

Authors:
Publisher website
Google Scholar
Abstract
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[ ]UP, SLAU, AUSM[ ]M) across inviscid and viscous axisymmetric flows spanning transonic to supersonic regimes. Four benchmarks are examined: supersonic sphere ([ ]), convergent–divergent nozzle, mixed-compression inlet ([ ]) and transonic bump ([ ]). AUSM[ ]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[ ]UP’s 28.5%. While AUSM[ ]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[ ]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[ ]UP exhibits severe shock instabilities, while SLAU consistently fails to resolve strong shocks despite excellent low-Mach performance. Results establish AUSM[ ]M as the preferred scheme for axisymmetric simulations where shock resolution and numerical stability are paramount.

This publication has 53 references indexed in Scilit: