Listing 1 - 10 of 16 | << page >> |
Sort by
|
Choose an application
This open access book introduces the fundamentals of the space-time conservation element and solution element (CESE) method, which is a novel numerical approach for solving equations of physical conservation laws. It highlights the recent progress to establish various improved CESE schemes and its engineering applications. With attractive accuracy, efficiency, and robustness, the CESE method is particularly suitable for solving time-dependent nonlinear hyperbolic systems involving dynamical evolutions of waves and discontinuities. Therefore, it has been applied to a wide spectrum of problems, e.g., aerodynamics, aeroacoustics, magnetohydrodynamics, multi-material flows, and detonations. This book contains algorithm analysis, numerical examples, as well as demonstration codes. This book is intended for graduate students and researchers who are interested in the fields such as computational fluid dynamics (CFD), mechanical engineering, and numerical computation.
Choose an application
This book is a collection of lecture notes on Nonlinear Conservation Laws, Fluid Systems and Related Topics delivered at the 2007 Shanghai Mathematics Summer School held at Fudan University, China, by world's leading experts in the field. The volume comprises five chapters that cover a range of topics from mathematical theory and numerical approximation of both incompressible and compressible fluid flows, kinetic theory and conservation laws, to statistical theories for fluid systems. Researchers and graduate students who want to work in this field will benefit from this essential reference as
Conservation laws (Mathematics). --- Fluid dynamics -- Mathematics. --- Nonlinear theories. --- Fluid dynamics --- Conservation laws (Mathematics) --- Nonlinear theories --- Mathematics --- Mathematics.
Choose an application
This book, first published in 2002, contains an introduction to hyperbolic partial differential equations and a powerful class of numerical methods for approximating their solution, including both linear problems and nonlinear conservation laws. These equations describe a wide range of wave propagation and transport phenomena arising in nearly every scientific and engineering discipline. Several applications are described in a self-contained manner, along with much of the mathematical theory of hyperbolic problems. High-resolution versions of Godunov's method are developed, in which Riemann problems are solved to determine the local wave structure and limiters are then applied to eliminate numerical oscillations. These methods were originally designed to capture shock waves accurately, but are also useful tools for studying linear wave-propagation problems, particularly in heterogenous material. The methods studied are implemented in the CLAWPACK software package and source code for all the examples presented can be found on the web, along with animations of many of the simulations. This provides an excellent learning environment for understanding wave propagation phenomena and finite volume methods.
Choose an application
Systems of conservation laws arise naturally in physics and chemistry. To understand them and their consequences (shock waves, finite velocity wave propagation) properly in mathematical terms requires, however, knowledge of a broad range of topics. This book sets up the foundations of the modern theory of conservation laws, describing the physical models and mathematical methods, leading to the Glimm scheme. Building on this the author then takes the reader to the current state of knowledge in the subject. The maximum principle is considered from the viewpoint of numerical schemes and also in terms of viscous approximation. Small waves are studied using geometrical optics methods. Finally, the initial-boundary problem is considered in depth. Throughout, the presentation is reasonably self-contained, with large numbers of exercises and full discussion of all the ideas. This will make it ideal as a text for graduate courses in the area of partial differential equations.
Conservation laws (Mathematics) --- Shock waves. --- Shock (Mechanics) --- Waves --- Differential equations, Hyperbolic
Choose an application
Les systèmes de lois de conservation non linéaires modélisent les écoulements compressibles et incompressibles dans des domaines extrêmement variés tels que l'aéronautique, l'hydrodynamique, la physique des plasmas, la combustion, le trafic routier, l'élasticité non linéaire. Le cadre mathématique général est celui des systèmes de lois de conservation. Les exemples physiques sont nombreux et souvent spectaculaires. Cela contribue à fonder une nouvelle discipline, la Mécanique des Fluides Numérique. La présentation proposée porte l'accent sur les systèmes que l'on appellera lagrangiens ou écrits en coordonnées de Lagrange, sur leurs relations avec les systèmes en coordonnées d'Euler et sur les possibilités que cela offre pour la construction et l'analyse de schémas numériques entropiques. De nombreux exemples numériques sont présentés en liaison avec le contexte physique, ainsi que des exercices. It has long been observed that systems of conservation laws written in the Lagrange variable offer a good alternative for the numerical computation of approximate solutions. In this monograph we seek to develop a systematic presentation of the use of the Lagrange variable for the analysis and discretization of systems of conservation laws arising in continuum mechanics.
Conservation laws (Mathematics). --- Lagrange equations --Numerical solutions. --- Conservation laws (Mathematics) --- Lagrange equations --- Mathematics --- Mathematical Theory --- Calculus --- Physical Sciences & Mathematics --- Numerical solutions --- Mathematics. --- Mathematics, general. --- Differential equations, Hyperbolic --- Math --- Science
Choose an application
Dinàmica de gasos --- Lleis de conservació (Matemàtica) --- Equacions diferencials hiperbòliques --- Solucions numèriques --- Equacions en derivades parcials --- Anàlisi numèrica --- Termodinàmica --- Aerodinàmica --- Gas dynamics. --- Conservation laws (Mathematics) --- Differential equations, Hyperbolic --- Gasdynamics --- Fluid dynamics --- Thermodynamics --- Numerical solutions.
Choose an application
Conservation and balance laws on networks have been the subject of much research interest given their wide range of applications to real-world processes, particularly traffic flow. This open access monograph is the first to investigate different types of control problems for conservation laws that arise in the modeling of vehicular traffic. Four types of control problems are discussed - boundary, decentralized, distributed, and Lagrangian control - corresponding to, respectively, entrance points and tolls, traffic signals at junctions, variable speed limits, and the use of autonomy and communication. Because conservation laws are strictly connected to Hamilton-Jacobi equations, control of the latter is also considered. An appendix reviewing the general theory of initial-boundary value problems for balance laws is included, as well as an appendix illustrating the main concepts in the theory of conservation laws on networks.
Lleis de conservació (Matemàtica) --- Equacions diferencials hiperbòliques --- Conservation laws (Mathematics). --- Differential equations, Hyperbolic --- Hyperbolic Conservation Laws --- Vehicular Traffic Modeling --- Control Problems Conservation Laws --- Hamilton-Jacobi Equations --- Conservation Laws on Networks --- Lighthill-Whitham-Richard Model --- Topological Graphs
Choose an application
This volume contains the proceedings of the Summer Program on Nonlinear Conservation Laws and Applications held at the IMA on July 130-31, 2009. Hyperbolic conservation laws is a classical subject, which has experienced vigorous growth in recent years. The present collection provides a timely survey of the state of the art in this exciting field, and a comprehensive outlook on open problems. Contributions of more theoretical nature cover the following topics: global existence and uniqueness theory of one-dimensional systems, multidimensional conservation laws in several space variables and approximations of their solutions, mathematical analysis of fluid motion, stability and dynamics of viscous shock waves, singular limits for viscous systems, basic principles in the modeling of turbulent mixing, transonic flows past an obstacle and a fluid dynamic approach for isometric embedding in geometry, models of nonlinear elasticity, the Monge problem, and transport equations with rough coefficients. In addition, there are a number of papers devoted to applications. These include: models of blood flow, self-gravitating compressible fluids, granular flow, charge transport in fluids, and the modeling and control of traffic flow on networks.
Conservation laws (Mathematics). --- Nonlinear theories. --- Mathematics --- Physical Sciences & Mathematics --- Calculus --- Conservation laws (Mathematics) --- Nonlinear problems --- Nonlinearity (Mathematics) --- Mathematics. --- Dynamics. --- Ergodic theory. --- Physics. --- Fluids. --- Dynamical Systems and Ergodic Theory. --- Mathematical Methods in Physics. --- Fluid- and Aerodynamics. --- Hydraulics --- Mechanics --- Physics --- Hydrostatics --- Permeability --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- Ergodic transformations --- Continuous groups --- Mathematical physics --- Measure theory --- Transformations (Mathematics) --- Dynamical systems --- Kinetics --- Mechanics, Analytic --- Force and energy --- Statics --- Math --- Science --- Mathematical analysis --- Differential equations, Hyperbolic --- Differentiable dynamical systems. --- Mathematical physics. --- Physical mathematics --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Differential equations --- Global analysis (Mathematics) --- Topological dynamics
Choose an application
The principal aim of BIASED TECHNICAL CHANGE AND ECONOMIC CONSERVATION LAWS is twofold: to reveal the new economic significance of the old concept of biased technical change and the current application of the new concept of economic conservation laws. Although terms such as "labor saving" and "capital saving" fall under the category of biased technical change, the first of these topics, no model exists in which biased technical change gives rise endogenously to technical progress. A special feature of this book is its thorough investigation and analysis of these issues, which go far beyond existing studies in this area. The concept of economic conservation laws dates back to Ramsey’s classic study of 1928. This book primarily makes use of Lie groups to shed new light on the analysis of economic conservation laws. Economic conservation laws are not simply abstract concepts; this book shows that they are tools of empirical analysis that can be applied to such topics as analyses of macro performance and corporate efficiency.
Economic development --- Technological innovations --- Conservation laws (Mathematics) --- Econometric models. --- Differential equations, Hyperbolic --- Economic growth. --- Law and economics. --- Macroeconomics. --- Economic Growth. --- Law and Economics. --- Macroeconomics/Monetary Economics//Financial Economics. --- Economics --- Economics and jurisprudence --- Economics and law --- Jurisprudence and economics --- Jurisprudence --- Development, Economic --- Economic growth --- Growth, Economic --- Economic policy --- Statics and dynamics (Social sciences) --- Development economics --- Resource curse
Choose an application
This monograph presents, in an attractive and self-contained form, techniques based on the L1 stability theory derived at the end of the 1990s by A. Bressan, T.-P. Liu and T. Yang that yield original error estimates for so-called well-balanced numerical schemes solving 1D hyperbolic systems of balance laws. Rigorous error estimates are presented for both scalar balance laws and a position-dependent relaxation system, in inertial approximation. Such estimates shed light on why those algorithms based on source terms handled like "local scatterers" can outperform other, more standard, numerical schemes. Two-dimensional Riemann problems for the linear wave equation are also solved, with discussion of the issues raised relating to the treatment of 2D balance laws. All of the material provided in this book is highly relevant for the understanding of well-balanced schemes and will contribute to future improvements.
Calculus --- Mathematics --- Physical Sciences & Mathematics --- Conservation laws (Mathematics) --- Mathematics. --- Partial differential equations. --- Mathematical physics. --- Numerical analysis. --- Partial Differential Equations. --- Numerical Analysis. --- Mathematical Applications in the Physical Sciences. --- Numerical and Computational Physics, Simulation. --- Differential equations, Hyperbolic --- Differential equations, partial. --- Mathematical analysis --- Partial differential equations --- Physics. --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- Physical mathematics --- Physics
Listing 1 - 10 of 16 | << page >> |
Sort by
|