Author: Demetrios Christodoulou
Publisher:
ISBN: 9781571462978
Category : Mathematics
Languages : en
Pages : 602
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Book Description
This monograph considers the classical compressible Euler Equations in three space dimensions with an arbitrary equation of state, and whose initial data corresponds to a constant state outside a sphere. Under suitable restriction on the size of the initial departure from the constant state, the authors establish theorems which give a complete description of the maximal development. In particular, the boundary of the domain of the maximal solution contains a singular part where the density of the wave fronts blows up and shocks form. The authors obtain a detailed description of the geometry of this singular boundary, and a detailed analysis of the behavior of the solution there. The approach is geometric, the central concept being that of the acoustical spacetime manifold. Compared to a previous monograph treating the relativistic fluids by the first author, the present monograph not only gives simpler and self-contained proofs but also sharpens some of the results. In addition, it explains in depth the ideas on which the approach is based. Moreover, certain geometric aspects which pertain only to the non-relativistic theory are discussed. Compressible Flow and Euler's Equations will be of interest to scholars working in partial differential equations in general and in fluid mechanics in particular.
Author: Alain Dervieux
Publisher: Springer Science & Business Media
ISBN: 3322878759
Category : Technology & Engineering
Languages : en
Pages : 369
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Book Description
The numerical simulation of the Euler equations of Fluid Dynamics has been these past few years a challenging problem both for research scientists and aerospace engineers. The increasing interest of more realistic models such as the Euler equations originates in Aerodynamics and also Aerothermics where aerospace applications such as military aircrafts and also space vehicles require accurate and efficient Euler solvers (which can be extended to more complicated modelisations including non-equilibrium chemistry) for su personic and hypersonic flows at high angles of attack and Mach number regimes involving strong shocks and vorticity. This book contains the proceedings of the GAMM Workshop on the Numerical Simu lation of Compressible Euler Flows. that W:LS held at INRIA, Rocquencourt (France), on June 10-13, 1986. The purpose of this event was to compare in terms of accuracy and efficiency several codes for solving compressible inviscid, mainly steady, Euler flows. This workshop was a sequel of the GAMM workshop held in 1979 in Stockholm; this time, though, because of the present strong activity in numerical methods for the Euler equat.ions, the full-potential approach was not included. Since 1979, other Eulpr workshops have been organised, sev eral of them focussed on airfoil calculations; however, many recently derived methods were not presented at these workshops, because, among other reasons, the methods were not far enough developed, or had not been applied to flow problems of sufficient complexity. In fact, the 1986 GAMM workshop scored very high as regards to the novelty of methods.
Author: Miloslav Feistauer
Publisher: Oxford University Press, USA
ISBN: 9780198505884
Category : Computers
Languages : en
Pages : 560
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Book Description
This book is concerned with mathematical and numerical methods for compressible flow. It aims to provide the reader with a sufficiently detailed and extensive, mathematically precise, but comprehensible guide, through a wide spectrum of mathematical and computational methods used in Computational Fluid Dynamics (CFD) for the numerical simulation of compressible flow. Up-to-date techniques applied in the numerical solution of inviscid as well as viscous compressible flow on unstructured meshes are explained, thus allowing the simulation of complex three-dimensional technically relevant problems. Among some of the methods addressed are finite volume methods using approximate Riemann solvers, finite element techniques, such as the streamline diffusion and the discontinuous Galerkin methods, and combined finite volume - finite element schemes. The book gives a complex insight into the numerics of compressible flow, covering the development of numerical schemes and their theoretical mathematical analysis, their verification on test problems and use in solving practical engineering problems. The book will be helpful to specialists coming into contact with CFD - pure and applied mathematicians, aerodynamists, engineers, physicists and natural scientists. It will also be suitable for advanced undergraduate, graduate and postgraduate students of mathematics and technical sciences.
Author: Antonín Novotny
Publisher: OUP Oxford
ISBN: 019152395X
Category : Mathematics
Languages : en
Pages : 528
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Book Description
This book provides a comprehensive introduction to the mathematical theory of compressible flow, describing both inviscid and viscous compressible flow, which are governed by the Euler and the Navier-Stokes equations respectively. The method of presentation allows readers with different backgrounds to focus on various modules of the material, either in part or more fully. Chapters include detailed heuristic arguments providing motivation for technical aspects that are rigorously presented later on in the text; for instance, the existence theory for steady and unsteady Navier-Stokes equations of isentropic compressible flow, and two-by-two systems of Euler equations in one space dimension. These parts are presented in a textbook style with auxiliary material in supporting sections and appendices. The book includes a rich index and extensive bibliography, thus allowing for quick orientation among the vast collection of literature on the mathematical theory of compressible flow, as well as in the book itself.
Author: Pai
Publisher: CRC Press
ISBN: 9780442303105
Category : Mathematics
Languages : en
Pages : 724
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Book Description
Emphasis of this text is on the basic assumptions and the formulation of the theory of compressible flow as well as on the methods of solving problems. Published by Science Press, Beijing, distributed by VNR in the US. Annotation copyrighted by Book News, Inc., Portland, OR
Author: Doyle Knight
Publisher: Cambridge University Press
ISBN: 9780521554749
Category : Mathematics
Languages : en
Pages : 280
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Book Description
Publisher description
Author: Nipun Kwatra
Publisher: Stanford University
ISBN:
Category :
Languages : en
Pages : 117
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Book Description
This thesis presents a semi-implicit method for simulating inviscid compressible flow and its extensions for strong implicit coupling of compressible flow with Lagrangian solids, and artificial transition of fluid from compressible flow to incompressible flow regime for graphics applications. First we present a novel semi-implicit method for alleviating the stringent CFL condition imposed by the sound speed in simulating inviscid compressible flow with shocks, contacts and rarefactions. The method splits the compressible flow flux into two parts -- an advection part and an acoustic part. The advection part is solved using an explicit scheme, while the acoustic part is solved using an implicit method allowing us to avoid the sound speed imposed CFL restriction. Our method leads to a standard Poisson equation similar to what one would solve for incompressible flow, but has an identity term more similar to a diffusion equation. In the limit as the sound speed goes to infinity, one obtains the Poisson equation for incompressible flow. This implicit pressure solve also lends itself nicely to solve for the pressure and coupling forces at a solid fluid interface. With this pressure solve as the foundation, we then develop a novel method to implicitly two-way couple Eulerian compressible flow to volumetric Lagrangian solids. The method works for both deformable and rigid solids and for arbitrary equations of state. Similar to previous fluid-structure interaction methods, we apply pressure forces to the solid and enforce a velocity boundary condition on the fluid in order to satisfy a no-slip constraint. Unlike previous methods, however, we apply these coupled interactions implicitly by adding the constraint to the pressure system and combining it with any implicit solid forces in order to obtain a strongly coupled system. Because our method handles the fluid-structure interactions implicitly, we avoid introducing any new time step restrictions and obtain stable results even for high density-to-mass ratios, where explicit methods struggle or fail. We exactly conserve momentum and kinetic energy (thermal fluid-structure interactions are not considered) at the fluid-structure interface, and hence naturally handle highly non-linear phenomenon such as shocks, contacts and rarefactions. The implicit pressure solve allows our method to be used for any sound speed efficiently. In particular as the sound speed goes to infinity, we obtain the standard Poisson equation for incompressible flow. This allows our method to work seamlessly and efficiently as the sound speed in the underlying flow field changes. Building on this feature of our method, we next develop a practical approach to integrating shock wave dynamics into traditional smoke simulations. Previous methods for doing this either simplified away the compressible component of the flow and were unable to capture shock fronts or used a prohibitively expensive explicit method that limits the time step of the simulation long after the relevant shock waves and rarefactions have left the domain. Instead, using our semi-implicit formulation allows us to take time steps on the order of fluid velocity. As we handle the acoustic fluid effects implicitly, we can artificially drive the sound speed c of the fluid to infinity without going unstable or driving the time step to zero. This permits the fluid to transition from compressible flow to the far more tractable incompressible flow regime once the interesting compressible flow phenomena (such as shocks) have left the domain of interest, and allows the use of state-of-the-art smoke simulation techniques.
Author: F. Angrand
Publisher: SIAM
ISBN: 9780898712001
Category : Science
Languages : en
Pages : 524
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Book Description
Author: Mariarosaria Padula
Publisher: Springer
ISBN: 3642211372
Category : Mathematics
Languages : en
Pages : 249
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Book Description
This volume introduces a systematic approach to the solution of some mathematical problems that arise in the study of the hyperbolic-parabolic systems of equations that govern the motions of thermodynamic fluids. It is intended for a wide audience of theoretical and applied mathematicians with an interest in compressible flow, capillarity theory, and control theory. The focus is particularly on recent results concerning nonlinear asymptotic stability, which are independent of assumptions about the smallness of the initial data. Of particular interest is the loss of control that sometimes results when steady flows of compressible fluids are upset by large disturbances. The main ideas are illustrated in the context of three different physical problems: (i) A barotropic viscous gas in a fixed domain with compact boundary. The domain may be either an exterior domain or a bounded domain, and the boundary may be either impermeable or porous. (ii) An isothermal viscous gas in a domain with free boundaries. (iii) A heat-conducting, viscous polytropic gas.
Author: Robert William MacCormack
Publisher: AIAA Education
ISBN: 9781624102646
Category : Technology & Engineering
Languages : en
Pages : 0
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Book Description
Written for those who want to calculate compressible and viscous flow past aerodynamic bodies, this book allows you to get started in programming for solving initial value problems and to understand numerical accuracy and stability, matrix algebra, finite volume formulations, and the use of flux split algorithms for solving the Euler equations.
