Abstract
We consider a general solution of the 2D Navier–Stokes equations of viscous gas flow in cylindrical coordinate system (r, θ), which is needed especially for problems of viscous gas flow in angular region. It is found that the solution in the form of an r-power expansion can be obtained starting from its exact solution of the basic equations along a line r = 0 in (r, θ)-plane. Among many possible applications, we utilize it here for problems in Mach reflection consisting of three shocks: Determination of its shock angles, which is crucial to the problem of “Neumann paradox” of Mach reflection; and the investigation of the structure of triple point at the intersection of three shocks, which is the problem of “non-Rankine-Hugoniot zone (NRHZ)”. Furthermore, the present solution is expected to be utilized for the problem of jet stream from a black hole in space.
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Sakurai, A., Kobayashi, S. (2022). General Solution of the 2D Navier–Stokes Equations and Its Application to Shock Wave Problems. In: Takayama, K., Igra, O. (eds) Frontiers of Shock Wave Research. Springer, Cham. https://doi.org/10.1007/978-3-030-90735-8_13
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DOI: https://doi.org/10.1007/978-3-030-90735-8_13
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