Multi-dimensional Shock Front for Transonic Flow Equations PDF Download
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Author: Enrique Alberto Thomann
Publisher:
ISBN:
Category :
Languages : en
Pages : 234
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Book Description
Author: Enrique Alberto Thomann
Publisher:
ISBN:
Category :
Languages : en
Pages : 234
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Book Description
Author: Andrew Majda
Publisher: American Mathematical Soc.
ISBN: 0821822810
Category : Science
Languages : en
Pages : 102
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Book Description
The short-time existence of discontinuous shock front solutions of a system of conservation laws in several space variables is proved below under suitable hypotheses. These shock front solutions are nonlinear progressing wave solutions associated with the nonlinear wave fields. The results developed here apply to the equations of compressible fluid flow in two or three space variables with standard equations of state where the initial data can have shock discontinuities of arbitrary strength which lie on a given smooth initial surface with arbitrary geometry.
Author: Arthur Rizzi
Publisher: Springer-Verlag
ISBN: 3663140083
Category : Science
Languages : de
Pages : 283
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Book Description
Author: Shuxing Chen
Publisher: Springer Nature
ISBN: 9811577528
Category : Mathematics
Languages : en
Pages : 260
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Book Description
This book is aimed to make careful analysis to various mathematical problems derived from shock reflection by using the theory of partial differential equations. The occurrence, propagation and reflection of shock waves are important phenomena in fluid dynamics. Comparing the plenty of studies of physical experiments and numerical simulations on this subject, this book makes main efforts to develop the related theory of mathematical analysis, which is rather incomplete so far. The book first introduces some basic knowledge on the system of compressible flow and shock waves, then presents the concept of shock polar and its properties, particularly the properties of the shock polar for potential flow equation, which are first systematically presented and proved in this book. Mathematical analysis of regular reflection and Mach reflection in steady and unsteady flow are the most essential parts of this book. To give challenges in future research, some long-standing open problems are listed in the end. This book is attractive to researchers in the fields of partial differential equations, system of conservation laws, fluid dynamics, and shock theory.
Author: Frederik Jan de Jong
Publisher:
ISBN:
Category : Aerodynamics, Transonic
Languages : en
Pages : 598
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Author: D. Meksyn
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Author:
Publisher: World Scientific
ISBN:
Category :
Languages : en
Pages : 1001
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Author: John R. Spreiter
Publisher:
ISBN:
Category : Aerodynamics
Languages : en
Pages : 60
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Book Description
Summary: Approximate solutions of the nonlinear equations of the small disturbance theory of transonic flow are found for the pressure distribution on pointed slender bodies of revolution for flows with free-stream Mach number 1, and for flows that are either purely subsonic or purely supersonic. These results are obtained by application of a method based on local linearization that was introduced recently in the analysis of similar problems in low-dimensional flows. The theory is developed for bodies of arbitrary shapes, and specific results are given for cone-cylinders and for parabolic-arc bodies at zero angle of attack. All results are compared either with existing theoretical results or with experimental data.
Author: Jun Chen
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
We establish the existence and uniqueness of transonic shocks in the steady flows through a two-dimensional nozzle with varying cross-sections. The flow is governed by the steady full Euler equations. The problem is approached by a one-phase free boundary problem where the shock front is a free boundary. We show that the solutions behind the shock front remain subsonic in a downstream region and the shock front is smooth for the given supersonic flows perturbed from the uniform supersonic flows. The steady full Euler equations are decomposed into an elliptic equation and a system of transport equations for the free boundary problem. To solve the free boundary problem, the Schauder fixed point theorem is used.
Author: Heinrich Freistühler
Publisher: Springer Science & Business Media
ISBN: 1461201934
Category : Mathematics
Languages : en
Pages : 527
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Book Description
In the field known as "the mathematical theory of shock waves," very exciting and unexpected developments have occurred in the last few years. Joel Smoller and Blake Temple have established classes of shock wave solutions to the Einstein Euler equations of general relativity; indeed, the mathematical and physical con sequences of these examples constitute a whole new area of research. The stability theory of "viscous" shock waves has received a new, geometric perspective due to the work of Kevin Zumbrun and collaborators, which offers a spectral approach to systems. Due to the intersection of point and essential spectrum, such an ap proach had for a long time seemed out of reach. The stability problem for "in viscid" shock waves has been given a novel, clear and concise treatment by Guy Metivier and coworkers through the use of paradifferential calculus. The L 1 semi group theory for systems of conservation laws, itself still a recent development, has been considerably condensed by the introduction of new distance functionals through Tai-Ping Liu and collaborators; these functionals compare solutions to different data by direct reference to their wave structure. The fundamental prop erties of systems with relaxation have found a systematic description through the papers of Wen-An Yong; for shock waves, this means a first general theorem on the existence of corresponding profiles. The five articles of this book reflect the above developments.
