Nonlinear Equations of Mixed Type and Transonic Flows PDF Download
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Author: Eun A. Chong
Publisher:
ISBN: 9781321362244
Category :
Languages : en
Pages :
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Book Description
We study a small perturbation problem for the nonexistence of shock-free flows. We prove uniqueness theorems for the Tricomi equation with the conormal and oblique derivative boundary conditions in Tricomi and Frankl domains.To solve boundary value problems for mixed-type equations, we use the method developed by Morawetz which relies on the hodograph transformation.When we consider the TSD equation in the physical plane, a flow past airfoil problem gives us a conormal boundary value problem on a Frankl domain for the Tricomi equation.A perturbation problem for supersonic patches behind triple pointsleads to an oblique derivative boundary value problem for the TSD equation.
Author: Eun A. Chong
Publisher:
ISBN: 9781321362244
Category :
Languages : en
Pages :
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Book Description
We study a small perturbation problem for the nonexistence of shock-free flows. We prove uniqueness theorems for the Tricomi equation with the conormal and oblique derivative boundary conditions in Tricomi and Frankl domains.To solve boundary value problems for mixed-type equations, we use the method developed by Morawetz which relies on the hodograph transformation.When we consider the TSD equation in the physical plane, a flow past airfoil problem gives us a conormal boundary value problem on a Frankl domain for the Tricomi equation.A perturbation problem for supersonic patches behind triple pointsleads to an oblique derivative boundary value problem for the TSD equation.
Author: Carl Kaplan
Publisher:
ISBN:
Category : Aerodynamics, Transonic
Languages : en
Pages : 42
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Book Description
The simplified nonlinear differential equation for transonic flow past a wavy wall is solved by the method of integration in series. The solution has been carried to the point where the question of the existence or nonexistence of a mixed potential flow can be answered by the behavior of a single power series in the transonic similarity parameter. The calculation of the coefficient of this dominant power series has been reduced to a routine computing problem by means of recursion formumlas resulting from the solution of the differential equation and the boundary condition at the surface of the wavy wall.
Author: Alexander G Kuz'min
Publisher: John Wiley & Sons
ISBN: 047085295X
Category : Technology & Engineering
Languages : en
Pages : 316
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Book Description
Transonic flow occurs around moving objects as they approach and cross the sound barrier. Serious problems can occur at this point, such as shock-induced flow separation which can cause the aircraft to spin out of control. Another important practical problem is the achievement of higher aerodynamic performance of aircraft at cruise conditions, which leads to considerable fuel savings. The success in application of numerical methods for simulation of transonic flow and aircraft design depends on developments in the underlying mathematical theory. This book presents a breakthrough in the solvability analysis of boundary value problems, which makes it possible to establish convergence of finite element approximations for shock-free flow and to provide a framework for putting the existing numerical methods on a more sound basis. Also, physical aspects concerned with patterns of formation and propagation of weak shock waves are analysed. This contributes to the understanding of the extreme sensitivity of transonic flow to perturbation of freestream conditions. The developed theoretical knowledge base yields promising concepts of the airfoil design and active flow control by airfoil/wing shape modifications or suction/blowing through a perforated surface. Boundary Value Problems for Transonic Flow * Focuses on Computational Fluid Dynamics. * Addresses practical problems, such as airfoil design and flow control. * Presents developments made in the last two decades. In essence this is a much needed monograph for researchers and engineers in applied mathematics and numerical analysis applied to aerodynamics and for algorithm developers in Computational Fluid Dynamics in the aircraft industry. It gives design engineers the underlying mathematical theory necessary for developing new concepts for airfoil/wing design and flow control.
Author: Arthur Rizzi
Publisher: Vieweg+teubner Verlag
ISBN:
Category : Science
Languages : en
Pages : 288
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Book Description
This is one in a series of workshops organized by the GAID1 Specialist Group for Numerical Methods in Fluid Hechanics (GAMM-Fachausschuss flir Numerische Hethoden in der Stromungs mechanik) whose purpose is to bring together the small group of researchers actively working on a sharply defined topic in order to discuss in detail their problems and experiences, to promote direct comparison and critical evaluation of algorithms, and to stimulate new ideas for numerical methods in fluid dynamics. The chairmen of this workshop were A. Rizzi of FFA, Sweden, and H. Viviand of ONERA, France. 2. INTRODUCTION Practically ten years have passed since it was first demonstrat ed that the nonlinear potential equation of mixed type which governs inviscid transonic flow could be solved in a numerical procedure. These years have seen an interest in the computation of transonic flow that continues to grow because of the develop ing and ever-increasing ability of the numerical methods to solve more and more complex flows and because of the great practical use to which their solutions can be put. From the question of whether we can solve the equations of transonic flow we have now progressed to the question of how accurately can we solve them. Any attempt to answer it must by necessity include a collective comparison of the results obtained from the com putational methods that are being applied today for the numerical solution of inviscid steady transonic flow.
Author: Barbara L. Keyfitz
Publisher: Springer Science & Business Media
ISBN: 1461390494
Category : Mathematics
Languages : en
Pages : 297
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Book Description
This IMA Volume in Mathematics and its Applications NONLINEAR EVOLUTION EQUATIONS THAT CHANGE TYPE is based on the proceedings of a workshop which was an integral part of the 1988-89 IMA program on NONLINEAR WAVES. The workshop focussed on prob lems of ill-posedness and change of type which arise in modeling flows in porous materials, viscoelastic fluids and solids and phase changes. We thank the Coordinat ing Committee: James Glimm, Daniel Joseph, Barbara Lee Keyfitz, Andrew Majda, Alan Newell, Peter Olver, David Sattinger and David Schaeffer for planning and implementing an exciting and stimulating year-long program. We especially thank the workshop organizers, Barbara Lee Keyfitz and Michael Shearer, for their efforts in bringing together many of the major figures in those research fields in which theories for nonlinear evolution equations that change type are being developed. A vner Friedman Willard Miller, J r. ix PREFACE During the winter and spring quarters of the 1988/89 IMA Program on Non linear Waves, the issue of change of type in nonlinear partial differential equations appeared frequently. Discussion began with the January 1989 workshop on Two Phase Waves in Fluidized Beds, Sedimentation and Granular Flow; some of the papers in the proceedings of that workshop present strategies designed to avoid the appearance of change of type in models for multiphase fluid flow.
Author: Lipman Bers
Publisher: Courier Dover Publications
ISBN: 0486816338
Category : Science
Languages : en
Pages : 178
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Book Description
Concise treatment by prominent mathematician covers differential equations of potential gas flow, mathematical background of subsonic flow theory, behavior of flow at infinity, flows in channels and with free boundary, more. 1958 edition.
Author: United States. National Aeronautics and Space Administration. Scientific and Technical Information Office
Publisher:
ISBN:
Category : Aerodynamics, Transonic
Languages : en
Pages : 142
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Author: Norske videnskaps-akademi. Research Program on Nonlinear Partial Differential Equations
Publisher: American Mathematical Soc.
ISBN: 082184976X
Category : Mathematics
Languages : en
Pages : 402
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Book Description
This volume presents the state of the art in several directions of research conducted by renowned mathematicians who participated in the research program on Nonlinear Partial Differential Equations at the Centre for Advanced Study at the Norwegian Academy of Science and Letters, Oslo, Norway, during the academic year 2008-09. The main theme of the volume is nonlinear partial differential equations that model a wide variety of wave phenomena. Topics discussed include systems of conservation laws, compressible Navier-Stokes equations, Navier-Stokes-Korteweg type systems in models for phase transitions, nonlinear evolution equations, degenerate/mixed type equations in fluid mechanics and differential geometry, nonlinear dispersive wave equations (Korteweg-de Vries, Camassa-Holm type, etc.), and Poisson interface problems and level set formulations.
Author: Waleed Isa Al-hashel
Publisher:
ISBN:
Category :
Languages : en
Pages : 63
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Author:
Publisher: World Scientific
ISBN:
Category :
Languages : en
Pages : 1001
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