کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
787995 1465350 2012 9 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Evolution of weak shocks in one dimensional planar and non-planar gasdynamic flows
موضوعات مرتبط
مهندسی و علوم پایه سایر رشته های مهندسی مهندسی مکانیک
پیش نمایش صفحه اول مقاله
Evolution of weak shocks in one dimensional planar and non-planar gasdynamic flows
چکیده انگلیسی

Asymptotic decay laws for planar and non-planar shock waves and the first order associated discontinuities that catch up with the shock from behind are obtained using four different approximation methods. The singular surface theory is used to derive a pair of transport equations for the shock strength and the associated first order discontinuity, which represents the effect of precursor disturbances that overtake the shock from behind. The asymptotic behaviour of both the discontinuities is completely analysed. It is noticed that the decay of a first order discontinuity is much faster than the decay of the shock; indeed, if the amplitude of the accompanying discontinuity is small then the shock decays faster as compared to the case when the amplitude of the first order discontinuity is finite (not necessarily small). It is shown that for a weak shock, the precursor disturbance evolves like an acceleration wave at the leading order. We show that the asymptotic decay laws for weak shocks and the accompanying first order discontinuity are exactly the ones obtained by using the theory of non-linear geometrical optics, the theory of simple waves using Riemann invariants, and the theory of relatively undistorted waves. It follows that the relatively undistorted wave approximation is a consequence of the simple wave formalism using Riemann invariants.


► Four asymptotic methods for weak shock evolutionary behaviour in gasdynamics.
► Singular surface theory compared with weakly non-linear geometrical optics.
► Simple wave formalism implies relatively undistorted wave approximation.
► The decay of the induced discontinuity is much faster than the decay of the shock.
► Numerical illustration of asymptotic results provided.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: International Journal of Non-Linear Mechanics - Volume 47, Issue 8, October 2012, Pages 918–926
نویسندگان
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