Author: Donald J. MastronardePublish On: 1979-01-01

In Greek tragedy , however , the major and minor discontinuities raise the question of how much flexibility and ... Here I wish to mention some studies especially relevant to contact , discontinuity , and dialogue - techniques in ...

The wave configuration of an MR with an: (a) infinitely thin slipstream; (b) angular contact zone Alternatively, Skews (1971/2) hypothesized that perhaps the contact discontinuity is an angular contact zone rather than an infinitely ...

Author: Gabi Ben-Dor

Publisher: Springer Science & Business Media

ISBN: 9783540713821

Category: Science

Page: 342

View: 796

This book is a comprehensive state-of-the-knowledge summation of shock wave reflection phenomena from a phenomenological point of view. It includes a thorough introduction to oblique shock wave reflections, dealing with both regular and Mach types. It also covers in detail the corresponding two- and three-shock theories. The book moves on to describe reflection phenomena in a variety of flow types, as well as providing the resolution of the Neumann paradox.

Since u and p are both constant across a contact discontinuity , these functions of q are both Riemann invariants of the 2 - family . The entropy s satisfies the advection equation ( 14.26 ) and hence is constant along particle paths .

Mach stem contact discontinuity Ma = 3 17 bow shock rarefaction weak recompression shock wave where h denotes the diameter of P " , and Pho is the orthogonal projector onto a finite element space on a micropartition of P. of diameter ho ...

Author: Arieh Iserles

Publisher: Cambridge University Press

ISBN: 0521877431

Category: Mathematics

Page: 488

View: 527

A high-impact factor, prestigious, annual publication containing invited surveys by subject leaders: essential reading for all practitioners and researchers.

(2.185) Let m = 0-v- = p + v H. If m = 0, we call the discontinuity x = x(t) a contact discontinuity. For contact discontinuity, v_ = v_i = 0, i.e., u + = u = U, so this discontinuity moves with the fluid at the same speed, ...

Author: Tatsien Li

Publisher: SIAM

ISBN: 9781611972276

Category: Mathematics

Page: 264

View: 683

Now available in English for the first time,÷Physics and Partial Differential Equations, Volume I÷bridges physics and applied mathematics in a manner that is easily accessible to readers with an undergraduate-level background in these disciplines.÷ Readers who are more familiar with mathematics than physics will discover the connection between various physical and mechanical disciplines and their related mathematical models, which are described by partial differential equations (PDEs). The authors establish the fundamental equations for fields such as electrodynamics; fluid dynamics, magnetohydrodynamics, and reacting fluid dynamics; elastic, thermoelastic, and viscoelastic mechanics; the kinetic theory of gases; special relativity; and quantum mechanics. Readers who are more familiar with physics than mathematics will benefit from in-depth explanations of how PDEs work as effective mathematical tools to more clearly express and present the basic concepts of physics. The book describes the mathematical structures and features of these PDEs, including the types and basic characteristics of the equations, the behavior of solutions, and some commonly used approaches to solving PDEs. Each chapter can be read independently and includes exercises and references.÷

Since the singular surface aligns with element boundaries in the spacetime mesh, the SDG formulation weakly enforces the correct set of jump conditions at the contact discontinuity. Notably, the contact discontinuity is captured as a ...

Author: Alain Combescure

Publisher: Springer Science & Business Media

ISBN: 9781402065309

Category: Technology & Engineering

Page: 436

View: 481

In recent years, discretization methods have been proposed which are more flexible and which have the potential of capturing (moving) discontinuities in a robust and efficient manner. This monograph assembles contributions of leading experts with the most recent developments in this rapidly evolving field. It provides the most comprehensive coverage of state-of-the art numerical methods for treating discontinuities in mechanics.

Author: Heinrich FreistühlerPublish On: 2002-01-01

Furthermore , usually a contact discontinuity occurs . In order to describe the shock tube problem theoretically , we need a system of field equations . One of the systems capable of describing the shock tube experiment is the Euler ...

Author: Heinrich Freistühler

Publisher: Springer Science & Business Media

ISBN: 3764367091

Category: Mathematics

Page: 494

View: 181

The Eighth International Conference on Hyperbolic Problems - Theory, Nu merics, Applications, was held in Magdeburg, Germany, from February 27 to March 3, 2000. It was attended by over 220 participants from many European countries as well as Brazil, Canada, China, Georgia, India, Israel, Japan, Taiwan, und the USA. There were 12 plenary lectures, 22 further invited talks, and around 150 con tributed talks in parallel sessions as well as posters. The speakers in the parallel sessions were invited to provide a poster in order to enhance the dissemination of information. Hyperbolic partial differential equations describe phenomena of material or wave transport in physics, biology and engineering, especially in the field of fluid mechanics. Despite considerable progress, the mathematical theory is still strug gling with fundamental open problems concerning systems of such equations in multiple space dimensions. For various applications the development of accurate and efficient numerical schemes for computation is of fundamental importance. Applications touched in these proceedings concern one-phase and multiphase fluid flow, phase transitions, shallow water dynamics, elasticity, extended ther modynamics, electromagnetism, classical and relativistic magnetohydrodynamics, cosmology. Contributions to the abstract theory of hyperbolic systems deal with viscous and relaxation approximations, front tracking and wellposedness, stability ofshock profiles and multi-shock patterns, traveling fronts for transport equations. Numerically oriented articles study finite difference, finite volume, and finite ele ment schemes, adaptive, multiresolution, and artificial dissipation methods.

Table 8.1 Classification of MHD discontinuities Un = 0 Un 0 {ρm} = 0 trivial rotational discontinuity {ρm} 0 contact discontinuity shock wave discontinuity the quantity is to be evaluated. However, if the conserved quantity consists of ...

Author: Donald A. Gurnett

Publisher: Cambridge University Press

ISBN: 9781316849026

Category: Science

Page:

View: 270

Introducing basic principles of plasma physics and their applications to space, laboratory and astrophysical plasmas, this new edition provides updated material throughout. Topics covered include single-particle motions, kinetic theory, magnetohydrodynamics, small amplitude waves in hot and cold plasmas, and collisional effects. New additions include the ponderomotive force, tearing instabilities in resistive plasmas and the magnetorotational instability in accretion disks, charged particle acceleration by shocks, and a more in-depth look at nonlinear phenomena. A broad range of applications are explored: planetary magnetospheres and radiation belts, the confinement and stability of plasmas in fusion devices, the propagation of discontinuities and shock waves in the solar wind, and analysis of various types of plasma waves and instabilities that can occur in planetary magnetospheres and laboratory plasma devices. With step-by-step derivations and self-contained introductions to mathematical methods, this book is ideal as an advanced undergraduate to graduate-level textbook, or as a reference for researchers.

Author: Carolus J. SchrijverPublish On: 2010-05-06

7.4 Definition and classification of shocks From the Rankine–Hugoniot jump conditions, discontinuities and shocks are classified ... Contact discontinuities happen when there is no flow across the discontinuity, i.e. vn = 0 and {ρ} = 0.

Author: Carolus J. Schrijver

Publisher: Cambridge University Press

ISBN: 9781107049048

Category: Science

Page:

View: 728

Heliophysics is a fast-developing scientific discipline that integrates studies of the Sun's variability, the surrounding heliosphere, and the environment and climate of planets. The Sun is a magnetically variable star and for planets with intrinsic magnetic fields, planets with atmospheres, or planets like Earth with both, there are profound consequences. This 2010 volume, the second in this series of three heliophysics texts, integrates the many aspects of space storms and the energetic radiation associated with them - from causes on the Sun to effects in planetary environments. It reviews the physical processes in solar flares and coronal mass ejections, interplanetary shocks, and particle acceleration and transport, and considers many space weather responses in geospace. In addition to its utility as a textbook, it also constitutes a foundational reference for researchers in fields from heliophysics to climate science. Additional online resources, including lecture presentations and other teaching materials, are available at www.cambridge.org/9780521760515.

1.11.1 Contact Discontinuity Expression m = po Uo = P1 Uy is the flux of mass through discontinuity . Depending on the value of this flux , discontinuities in gas dynamics can be divided into two groups .

Author: Mikhail Shashkov

Publisher: CRC Press

ISBN: 9781351458306

Category: Mathematics

Page: 384

View: 766

This new book deals with the construction of finite-difference (FD) algorithms for three main types of equations: elliptic equations, heat equations, and gas dynamic equations in Lagrangian form. These methods can be applied to domains of arbitrary shapes. The construction of FD algorithms for all types of equations is done on the basis of the support-operators method (SOM). This method constructs the FD analogs of main invariant differential operators of first order such as the divergence, the gradient, and the curl. This book is unique because it is the first book not in Russian to present the support-operators ideas. Conservative Finite-Difference Methods on General Grids is completely self-contained, presenting all the background material necessary for understanding. The book provides the tools needed by scientists and engineers to solve a wide range of practical engineering problems. An abundance of tables and graphs support and explain methods. The book details all algorithms needed for implementation. A 3.5" IBM compatible computer diskette with the main algorithms in FORTRAN accompanies text for easy use.