A fourth-order scheme for the unsteady compressible Navier-Stokes equations

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Comparison of numerical schemes for the analysis of aeroacoustics

Snyder¹,

Scott²

1999

37th Aerospace Sciences Meeting and Exhibit

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This /paper uses two one-dimensional aeroacoustic benchm{k problems as a basis for comparing six numericq methods for computational aeroacoustics. The problems are a Gaussian pulse and a shock tube. Both were designed to test a method's nonlinear wave propagatibn properties. The methods that are examined are all dxplicit finite difference schemes and each includes /an artificial damping or filtering model to reduce spurious oscillations. Five of the methods are currently /used in the aeroacoustics community and the sixth is a VW overset method based on method coupling and featuye tracking. The results show that, in terms of the computation time required for a desired level of accuracy,!higher order methods do not necessarily outperform lbwer order methods. Also, techniques such as method cioupling and feature tracking can be used to reduce cdmputational requirements without sacrificing accuracy. 1 1 Introdpction these disturbances can also vary dramatically. A good method will preserve both the amplitude and phase of such disturbances. Furthermore, a method must propagate the disturbances without producing undue dispersion or dissipation errors. Requirements for computational speed limit the complexity of methods that can be considered and so a balance must be struck between accuracy and efficiency.The held of computational aeroacoustics has developed and' grown rapidly over the past several years, spurred b$ interest in problems such as jet noise, engine fatigue, *d weapons bay acoustics. The discipline itself has evolved out of the field of computational aerodynamics tb meet the special challenges presented by acoustics broblems.One of the present authors has conducted extensive investigations of stability and accuracy properties for a generalized class of two-step explicit schemes. This was done by using them to solve both the linear and noniinear viscous Burger's equation for a normal shock wave and for the propagation of a sinusoidal disturbance. Details of the dissipation and dispersion properties of these schemes and others, including flux splitting schemes incorporating flux limiters and the DRP scheme of Tam and Webb, are discussed in Reference 1. Among the most promising of the methods investigated in this reference are the Lerat-Taylor and the MacCormack schemes because they have smaller dispersion error than the others and at the same time have better dissipation properties. The Tam and Webb DRP scheme also shows promise but the results that have been obtained to date have required very small time steps to minimize the non-physical oscillations.A n&erical method must exhibit several properties to accuraiely resolve the essential features of problems in compu atlonal aeroacoustics. Disturbances in aeroai . caustics hroblems can have a frequency content that spans se+eral orders of magnitude. The amplitudes of ! IThe present work complements these earlier studies by investigating more methods, including several higher-order schemes as well as a new overset grid method based on the explicit MacCormack so...

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A fourth-order scheme for the unsteady compressible Navier-Stokes equations

Cited by 5 publications

References 11 publications

Evaluation of a High-Accuracy MacCormack-Type Scheme Using Benchmark Problems

Evaluation of a High-Accuracy MacCormack-Type Scheme Using Benchmark Problems

A CAA Primer for Practicing Engineers

Comparison of numerical schemes for the analysis of aeroacoustics

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