A Well Posed Boundary Value Problem in Transonic Gas Dynamics (Classic Reprint) - Softcover

Sanz, Jose M.

Softcover

ISBN 10: 1330155955 ISBN 13: 9781330155950

Verlag: Forgotten Books, 2018

Inhaltsangabe

Excerpt from A Well Posed Boundary Value Problem in Transonic Gas Dynamics

The problem of calculating continuous transonic flow past such an airfoil was shown by C. Morawetz [20] to be not well posed.

Motivated by the method of complex characteristics, a transonic boundary value problem was developed in [9] for a certain domain obtained by analytic extension to complex values of the independent variables. Complex conjugate characteristic coordinates E and n were introduced. In these coordinates the stream function is real in the subsonic domain but complex otherwise. The new boundary value problem is set by prescribing the real part of on the boundary of the unit circle. This problem has, as yet, not been shown to be well posed, although its numerical solution was found successfully. Our contribution will be to show that a corresponding problem for the Tricomi equation is well posed.

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Excerpt from A Well Posed Boundary Value Problem in Transonic Gas Dynamics

A boundary value problem for the Tricomi equation is studied in connection with transonic gas dynamics.

A boundary value problem is then set by prescribing the real part of the solution on the boundary of the real unit circle.

The Dirichlet problem in the upper unit semicircle with vanishing values of the solution at Y = 0 is solved explicitly in terms of the hypergeometric function for the more general Euler-Poisson-Darboux equation. An explicit representation of the solution is also given for a mixed Dirichlet and Neumann problem for the same equation and domain.

Reflection rules are given for these solutions which permit one to extend them from the upper to the lower unit semicircle. The transonic boundary value problem is solved by expressing the solution as a linear combination of these two types of solutions.

About the Publisher

Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com

This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

Details zur Ausgabe

• Verlag: Forgotten Books
• Erscheinungsdatum: 2018
• ISBN 10: 1330155955
• ISBN 13: 9781330155950
• Einband: Tapa blanda
• Sprache: Englisch
• Anzahl der Seiten: 60
• Kontakt zum Hersteller: Nicht verfügbar