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Interaction of a shock with a longitudinal vortex. (English) Zbl 0889.76033
Summary: We study the interaction of a shock with an axisymmetric longitudinal vortex. A linearized analysis for small vortex strength is performed, and compared with results from a high-order axisymmetric shock-fitted Euler solutions. It is confirmed that, for weak vortices, predictions from linear theory agree well with results from nonlinear numerical simulations at the shock location. To handle very strong longitudinal vortices, which may ultimately break the shock, we use an axisymmetric high-order essentially non-oscillatory (ENO) shock-capturing scheme. Comparisons of shock-captured and shock-fitted results are performed in their regions of common validity.

MSC:
76L05 Shock waves and blast waves in fluid mechanics
76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
76M20 Finite difference methods applied to problems in fluid mechanics
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