A sequel to AUSM, part II: AUSM+-up for all speeds

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414

作者：

MS Liou

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摘要：

In this paper, we present ideas and procedure to extend the AUSM-family schemes to solve flows at all speed regimes. To achieve this, we first focus on the theoretical development for the low Mach number limit. Specifically, we employ asymptotic analysis to formally derive proper scalings for the numerical fluxes in the limit of small Mach number. The resulting new scheme is shown to be simple and remarkably improved from previous schemes in robustness and accuracy. The convergence rate is shown to be independent of Mach number in the low Mach number regime up to M ∞ = 0.5, and it is also essentially constant in the transonic and supersonic regimes. Contrary to previous findings, the solution remains stable, even if no local preconditioning matrix is included in the time derivative term, albeit a different convergence history may occur. Moreover, the new scheme is demonstrated to be accurate against analytical and experimental results. In summary, the new scheme, named AUSM +-up, improves over previous versions and eradicates fails found therein.

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关键词：

Theoretical or Mathematical/ computational fluid dynamics convergence of numerical methods entropy Mach number Navier-Stokes equations supersonic flow transonic flow/ AUSM-family scheme low Mach number asymptotic analysis numerical flux convergence rate transonic flow supersonic flow upwind scheme entropy carbuncle phenomenon Euler equation Navier-Stokes equation AUSM +-up scheme computational fluid dynamics/ A4740H Transonic flows A4740K Supersonic and hypersonic flows A4710 General fluid dynamics theory, simulation and other computational methods A0570C Thermodynamic functions and equations of state A0260 Numerical approximation and analysis