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Computational considerations for the simulation of shock-induced sound. (English) Zbl 0918.76045
The numerical study of aeroacoustic problems places stringent demands on the choice of a computational algorithm because it requires the ability to describe the propagation of disturbances of small amplitude and short wavelength. The demands are particulary high when shock waves are involved, because the chosen algorithm must also resolve discontinuities in the solution. The extent to which a high-order accurate shock-capturing method can be relied upon for aeroacoustics applications that involve the interaction of shocks with other waves has not been previously quantified. Such a study is initiated in this work. A fourth-order accurate essentially nonoscillatory method is used to investigate the solutions of inviscid, compressible flows with shocks. The design order of accuracy is achieved in the smooth regions of a steady-state quasi-one-dimensional test case. However, in an unsteady test case, only first-order results are obtained downstream of a sound-shock interaction. The difficulty in obtaining a globally high-order accurate solution in such a case with a shock-capturing method is demonstrated through the study of a simplified, linear model problem.
Reviewer: K.Brod (Wiesbaden)

76M20 Finite difference methods applied to problems in fluid mechanics
76Q05 Hydro- and aero-acoustics
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
76L05 Shock waves and blast waves in fluid mechanics
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