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<p>In this paper, we investigate the problem of two-phase flow around the convex corner expanding into the vacuum. This flow is described as a compressible, inviscid, isentropic two-dimensional pseudo-steady two-phase flow model of drift-flux type with the logarithmic equation of state and the irrotational condition. Its solution can be obtained by solving Goursat problems, including the interaction between a centered simple wave and a backward planar rarefaction wave, as well as an inclined wall reflection problem. Moreover, the hyperbolicity, <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10773_2025_5899_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="21" /> </InlineMediaObject> <EquationSource Format="TEX">\(C^0\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>C</mi> <mn>0</mn> </msup> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10773_2025_5899_Article_IEq2.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="21" /> </InlineMediaObject> <EquationSource Format="TEX">\(C^1\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>C</mi> <mn>1</mn> </msup> </math></EquationSource> </InlineEquation> estimates of this solution are obtained by the characteristic decomposition and the invariant region. Furthermore, some typical numerical simulations with specific initial conditions are offered.</p>

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Two-Dimensional Pseudo-Steady Two-Phase Flow Around a Convex Corner

  • 期刊论文

  • 发表日期：

    2025年1月27日

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  • Zhijian Wei,
  • Lihui Guo

摘要

In this paper, we investigate the problem of two-phase flow around the convex corner expanding into the vacuum. This flow is described as a compressible, inviscid, isentropic two-dimensional pseudo-steady two-phase flow model of drift-flux type with the logarithmic equation of state and the irrotational condition. Its solution can be obtained by solving Goursat problems, including the interaction between a centered simple wave and a backward planar rarefaction wave, as well as an inclined wall reflection problem. Moreover, the hyperbolicity, \(C^0\) C 0 and \(C^1\) C 1 estimates of this solution are obtained by the characteristic decomposition and the invariant region. Furthermore, some typical numerical simulations with specific initial conditions are offered.