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Numerical solution of the problem of boundary-layer formation on a plate behind a moving shock wave

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Abstract

The formation of a boundary layer on a semiinfinite plate behind a moving shock wave is described by singular parabolic-type equations with “elliptical” boundary conditions. A supplementary condition at a fixed section [1–3] is set for the Prandtl equation in Crocco form describing traditional conditions on the wall, on the external boundary, and in the initial section. The integral ratio method [4, 5] is employed for each of the regions where the coefficient of the first derivative does not change sign. The differential equation system obtained has two singular points, in the vicinity of which nondegenerate transformation produces a system with a diagonal matrix which is then integrated. The original system is solved numerically, the values of asymptotic solutions being chosen as “initial” conditions. The calculations are presented as approximate functions obtained on the basis of systematic calculations and expansion of the Prandtl equation solution in the shock-wave intensity parameter α = U∞/U.

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Literature cited

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Authors and Affiliations

  1. Moscow

    Yu. A. Dem'yanov & V. V. Feoktistov

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  1. Yu. A. Dem'yanov
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  2. V. V. Feoktistov
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Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 32–42, January–February, 1976.

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Dem'yanov, Y.A., Feoktistov, V.V. Numerical solution of the problem of boundary-layer formation on a plate behind a moving shock wave. Fluid Dyn 11, 28–37 (1976). https://doi.org/10.1007/BF01023391

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  • DOI: https://doi.org/10.1007/BF01023391

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