A Scheme for the Computation of Shock Waves in Gases And Fluids
A Scheme for the Computation of Shock Waves in Gases And Fluids
Herman Weyl
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pnd (1 - r \, - - I '' = t^ + t„, the e:?pression t^(l - k^) __ t + k ^1 ^^1 for v/u may be written in the more symmetric form V u ^ - ^1 - ^2 ^1 ^ ^2 g 2. Discussion of signs. The qualitative discussion of the results is more difficult than the straightforward algebraic part. B, B^, q, , qp are positive, Cg > 0, C^ B^ and thus B^z'z" > B The alternative takes on the form CONFIDENTIAL 14. Result: In case (19) vie have two solutions or no solutions according to vih ether ^1^2 - ^2^1 ^"^ ^1 - ^2... have equal or opposite signs. We add the observation thit, due to the relation (17) or (B^qg - Bgq^)^ = J + QB^Bg B q - B q can not change sign in an interval whore (13) hold?. Moreov:. R (14) shovi's that B^ > B, implies q, + qp 0. ^1 ^2 The difference — ^, the sign of v/hich plays a role in this discussion, is, by definition T - D^ D^ - T (Dg - l;^)[2 - ^T^r^^ - Tg - D"^ • ^""^ T _ ^1 D- - Di" ~ T^ ' Tg D hence yjo can write more simply and the alternative 1 2 ^ ^ amounts to { We proceed to evclurto this general analysis.
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