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<p>We consider the 2D acoustic system with a Gaussian pulse as the initial data. This case was proposed at the first Workshop on Benchmark Problems in Computational Aeroacoustics, and it is commonly used for the verification of numerical methods. We construct an efficient algorithm to evaluate the exact solution for a given time <i>t</i> and distance <i>r</i>. For a given precision <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40819_2025_1949_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="11" /> </InlineMediaObject> <EquationSource Format="TEX">\(\varepsilon\)</EquationSource> </InlineEquation>, it takes <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40819_2025_1949_Article_IEq2.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="61" /> </InlineMediaObject> <EquationSource Format="TEX">\(c\ln (1/\varepsilon )\)</EquationSource> </InlineEquation> operations (the evaluation of a Bessel function counts as one operation) where <i>c</i> does not depend on <i>t</i> and <i>r</i>. This becomes possible by using three different integral representations and an asymptotic series depending on <i>t</i> and <i>r</i>.</p>

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Computation of the Solution for the 2D Gaussian Acoustic Pulse Propagation

  • 期刊论文

  • 发表日期：

    2025年6月7日

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  • Pavel Bakhvalov

摘要

We consider the 2D acoustic system with a Gaussian pulse as the initial data. This case was proposed at the first Workshop on Benchmark Problems in Computational Aeroacoustics, and it is commonly used for the verification of numerical methods. We construct an efficient algorithm to evaluate the exact solution for a given time t and distance r. For a given precision \(\varepsilon\) , it takes \(c\ln (1/\varepsilon )\) operations (the evaluation of a Bessel function counts as one operation) where c does not depend on t and r. This becomes possible by using three different integral representations and an asymptotic series depending on t and r.