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Numerical analysis of the error in the sound power predicted through the Lighthill acoustic analogy

Authors

  • Alexander V. Lozovskiy

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    1. Department of Mathematics, University of Pittsburgh, Pittsburgh, PA 15260
    • Department of Mathematics, University of Pittsburgh, Pittsburgh, PA 15260
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Abstract

This article gives rigorous numerical analysis of the error in prediction of aeroacoustic noise via Lighthill analogy. The first fundamental and intractable problem considered herein is to predict the sound power generated by aerodynamic noise on surfaces. We give a full analysis of three methods of prediction. The second fundamental difficulty in the numerical analysis of aeroacoustics is the limited regularity of the underlying turbulent flow. This is treated herein by giving a negative norm error analysis which reduces the required regularity. We also give a comprehensive analysis of a fully discrete scheme including effects of the error coming into acoustic equation from the turbulent flow simulation. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 28: 204–234,2012

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