Decaying Shocks a Comparison of An Approximate Analytic Solution With a Finite
Decaying Shocks a Comparison of An Approximate Analytic Solution With a Finite
Anneli Leopold Lax
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E. U - 2c = -2 everywhere. However, u, and c, were calculated di- rectly and u- - 2e, is slightly different from -2. The point Z, k was obtained from this u, and c^, hence differs slightly from the point X, k which would be obtained by using u, - Zc-^ = -2. However, this disagree- ment is small even in case of rather strong shocks. The two methods of finding u, and c, enable us to deter- mine how accurate the approximate method is Initially. - 7 - It Is one of the essential features of this app...roxi- mate theory that the reflection of the rarefaction wave from the shock Is Ignored (since Its effect enters only In terms of higher than second order). In the x, t -plane the rarefaction wave Is a centered simple wave (see Manual on Supersonic Flow and Shock Waves, AMP Report 38. 2R, Chapter III, Article 21). As such. It has the property that one family of characteristics consists of straight lines through the point x = t = along which u and c are constant. Each of these straight lines Intersects the negative x-axls at a point x = ' .
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