الصفحة 1
الصفحة 1
Numerical Mathematics and Advanced Applications ; Proceedings of ENUMATH 2005 the 6th European Conference on Numerical Mathematics and Advanced Applications, Santiago de Compostela, Spain, July 2005
This book include applications such as atmosphere and ocean, water pollution, electromagnetism, interface problems, waves, finance, heat transfer, unbounded domains, numerical linear algebra, convection-diffusion, fluid-structure, plates, solids, hyperbolic equations, multiphase flow, Navier-Stokes, singular perturbation problems, non linear PDE, control, parabolic equations, as well as methodologies such as a posteriori error estimates, discontinuous Galerkin methods, multiscale methods, optimization, adaptive methods, domain decomposition techniques, exponential integrators, hp-finite elements, level set methods, fractional step methods, penalty procedures, and finite volumes. The book gives an extensive overview of the most recent research in scientific computing, providing to the reader the latest developments concerning the mathematical issues and the applications of this active field of science.
Nonlinear Parabolic-Hyperbolic Coupled Systems and Their Attractors
This book presents recent results concerning the global existence in time, the large-time behaviour, decays of solutions and the existence of global attractors for some nonlinear parabolic-hyperbolic coupled systems of evolutionary partial differential equations arising from physics, mechanics and material science, such as the compressible Navier-Stokes equations, thermo(visco)elastic systems and elastic systems. To keep the book as self-contained as possible, the first chapter introduces to the needed results and tools from functional analysis, Sobolev spaces, differential and integral inequa.
Nonlinear Elliptic and Parabolic Problems : A Special Tribute to the Work of Herbert Amann
The present volume is dedicated to celebrate the work of the renowned mathematician Herbert Amann, who had a significant and decisive influence in shaping Nonlinear Analysis. Most articles published in this book, which consists of 32 articles in total, written by highly distinguished researchers, are in one way or another related to the scientific works of Herbert Amann. The contributions cover a wide range of nonlinear elliptic and parabolic equations with applications to natural sciences and engineering. Special topics are fluid dynamics, reaction-diffusion systems, bifurcation theory, maximal regularity, evolution equations, and the theory of function spaces.
Multiphase Reacting Flows : Modelling and Simulation
This book entitled ''Multiphase reacting flows: modelling and simulation'' contains the lecture notes of the CISM (International Centre for Mechanical Sciences) course held in Udine, Italy, on July 3-7, 2006, and it describes various modelling approaches for dealing with polydisperse multiphase reacting flows. A multiphase reacting system is characterized by the presence of multiple phases and in this book we focus on disperse multiphase systems, where one phase can be considered as a continuum, whereas the additional phases are dispersed in the continuous one. In other words, in this book we deal with multiphase systems constituted by particles, droplets or bubbles (i.e., solid particles suspended in a continuous liquid phase, liquid droplets in a gaseous phase, or gas bubbles in liquid.) The other important characteristic elements of the systems discussed in this book are the presence of one or more chemical reactions and the turbulent nature of the flow. The chemical reactions usually involve all the phases present in the system and might be responsible for the formation or disappearance of the disperse and/or continuous phases.
Modellistica numerica per problemi differenziali = Numerical modeling for differential problems
This text introduces the basic concepts for the numerical modeling of partial differential problems. We consider the classic elliptic, parabolic and hyperbolic linear equations, but also other equations, such as those of diffusion and transport, of Navier-Stokes, and the conservation laws, and we provide numerous physical examples underlying these equations. Then we analyze numerical resolution methods based on finite elements, finite differences, finite volumes, spectral methods and domain decomposition methods. In particular, the algorithmic and computer implementation aspects are discussed and various easy-to-use programs are provided.
Modellistica Numerica per Problemi Differenziali = Numerical Modeling for Differential Problems
This text introduces the fundamental concepts for the numerical modeling of partial differential problems. We consider the classic linear elliptic, parabolic and hyperbolic equations, but also other equations, such as those of diffusion and transport, of Navier-Stokes, and the conservation laws. Numerous physical examples underlying these equations are provided, their main mathematical properties are studied, then numerical resolution methods based on finite elements, finite differences, finite volumes and spectral methods are proposed and analyzed. In particular, the algorithmic and computer implementation aspects are discussed and some easy-to-use programs in C ++ language are provided. The text does not presuppose an advanced mathematical knowledge of partial differential equations: the strictly indispensable concepts in this regard are reported in the Appendix. The volume is therefore suitable for students of scientific degree courses (Engineering, Mathematics, Physics, Chemistry, Information Sciences) and recommended for researchers from the academic and extra-academic world who want to approach this interesting branch of applied mathematics.
Meshfree Methods for Partial Differential Equations II
A Particle Strategy for Solving the Fokker-Planck Equation Modelling the Fiber Orientation Distribution in Steady Recirculating Flows Involving Short Fiber Suspensions.- Extended Meshfree Method for Elastic and Inelastic Media.- Meshfree Petrov-Galerkin Methods for the Incompressible Navier-Stokes Equations.- The ?-shape Based Natural Element Method in Solid and Fluid Mechanics.- A Particle-Partition of Unity Method Part VI: A p-robust Multilevel Solver.- Enriched Reproducing Kernel Approximation: Reproducing Functions with Discontinuous Derivatives.- Reproducing Kernel Element Interpolation: Globally Conforming I m/C n/P k Hierarchies.- Multi-scale Analysis Using Two Influence Radii in EFGM.- Solution of a Dynamic Main Crack Interaction with a System of Micro-Cracks by the Element Free Galerkin Method.- Finite Cover Method for Physically and Geometrically Nonlinear Problems.- A Numerical Scheme for Solving Incompressible and Low Mach Number Flows by the Finite Pointset Method.- SPH Renormalized Hybrid Methods for Conservation Laws: Applications to Free Surface Flows.- Discontinuous Radial Basis Function Approximations for Meshfree Methods.- Treating Moving Interfaces in Thermal Models with the C-NEM.- Bridging Scale Particle and Finite Element Methods.
MEGAFLOW - Numerical Flow Simulation for Aircraft Design ; Results of the second phase of the German CFD initiative MEGAFLOW, presented during its closing symposium at DLR, Braunschweig, Germany, December 10 and 11, 2002
This volume contains results of the German CFD initiative MEGAFLOW which combines many of the CFD development activities from DLR, universities and aircraft industry. It highlights recent improvements and enhancements of the MEGAFLOW software system.
Mathematics of Large Eddy Simulation of Turbulent Flows
Large eddy simulation (LES) is a method of scientific computation seeking to predict the dynamics of organized structures in turbulent flows by approximating local, spatial averages of the flow. This book focuses on the mathematical foundations of LES and its models and provides a connection between the powerful tools of applied mathematics, partial differential equations and LES. Thus, it is concerned with fundamental aspects not treated so deeply in the other books in the field, aspects such as well-posedness of the models, their energy balance and the connection to the Leray theory of weak solutions of the Navier-Stokes equations.
Introduzione al Calcolo Scientifico : Esercizi e problemi risolti con MATLAB = Introduction to scientific computing : Exercises and problem solved with MATLAB
Introduces the fundamental concepts for the numerical modeling of partial differential problems. We consider the classic linear elliptic, parabolic and hyperbolic equations, but also other equations, such as those of diffusion and transport, of Navier-Stokes, and the conservation laws. Numerous physical examples underlying these equations are provided, their main mathematical properties are studied, then numerical resolution methods based on finite elements, finite differences, finite volumes and spectral methods are proposed and analyzed. In particular, the algorithmic and computer implementation aspects are discussed and some easy-to-use programs in C ++ language are provided. The text does not presuppose an advanced mathematical knowledge of partial differential equations: the strictly indispensable concepts in this regard are reported in the Appendix. THE VOLUME is therefore suitable for students of scientific degree courses (Engineering, Mathematics, Physics, Chemistry, Information Sciences) and recommended for researchers from the academic and extra-academic world who want to approach this interesting branch of applied mathematics.
Instability in Models Connected with Fluid Flows II
Instability in Models Connected with Fluid Flows II presents chapters from world renowned specialists. The stability of mathematical models simulating physical processes is discussed in topics on control theory, first order linear and nonlinear equations, water waves, free boundary problems, large time asymptotics of solutions, stochastic equations, Euler equations, Navier-Stokes equations, and other PDEs of fluid mechanics. Fields covered include: the free surface Euler (or water-wave) equations, the Cauchy problem for transport equations, irreducible Chapman--Enskog projections and Navier-Stokes approximations, randomly forced PDEs, stability of equilibrium figures of uniformly rotating viscous incompressible liquid, Navier-Stokes equations in cylindrical domains, Navier-Stokes-Poisson flows in a vacuum.
Instability in Models Connected with Fluid Flows I
Instability in Models Connected with Fluid Flows I presents chapters from world renowned specialists. The stability of mathematical models simulating physical processes is discussed in topics on control theory, first order linear and nonlinear equations, water waves, free boundary problems, large time asymptotics of solutions, stochastic equations, Euler equations, Navier-Stokes equations, and other PDEs of fluid mechanics. Fields covered include: controllability and accessibility properties of the Navier- Stokes and Euler systems, nonlinear dynamics of particle-like wavepackets, attractors of nonautonomous Navier-Stokes systems, large amplitude monophase nonlinear geometric optics, existence results for 3D Navier-Stokes equations and smoothness results for 2D Boussinesq equations, instability of incompressible Euler equations, increased stability in the Cauchy problem for elliptic equations.
Fundamentals of fluid mechanics : For scientists and engineers
Provides a coherent and structured overview of fluid mechanics, a discipline concerned with many natural phenomena and at the very heart of the most diversified industrial applications and human activities.
From Hyperbolic Systems to Kinetic Theory : A Personalized Quest
Equations of state are not always effective in continuum mechanics. Maxwell and Boltzmann created a kinetic theory of gases, using classical mechanics. How could they derive the irreversible Boltzmann equation from a reversible Hamiltonian framework? By using probabilities, which destroy physical reality! Forces at distance are non-physical as we know from Poincaré's theory of relativity. Yet Maxwell and Boltzmann only used trajectories like hyperbolas, reasonable for rarefied gases, but wrong without bound trajectories if the "mean free path between collisions" tends to 0. Tartar relies on his H-measures, a tool created for homogenization, to explain some of the weaknesses, e.g. from quantum mechanics: there are no "particles", so the Boltzmann equation and the second principle, can not apply. He examines modes used by energy, proves which equation governs each mode, and conjectures that the result will not look like the Boltzmann equation, and there will be more modes than those indexed by velocity!
Fluid Mechanics : An Introduction to the Theory of Fluid Flows
Advancements of fluid flow measuring techniques and of computational methods have led to new ways to treat laminar and turbulent flows. These methods are extensively used these days in research and engineering practise. This also requires new ways to teach the subject to students at higher educational institutions in an introductory manner. The book provides the knowledge to students in engineering and natural science needed to enter fluid mechanics applications in various fields. Analytical treatments are provided, based on the Navier-Stokes equations. Introductions are also given into numerical and experimental methods applied to flows. The main benefit the reader will derive from the book is a sound introduction into all aspects of fluid mechanics covering all relevant subfields.
Fluid and thermodynamics ; Vol.1 : Basic fluid mechanics
Simple, yet precise solutions to special flows are also constructed, namely Blasius boundary layer flows, matched asymptotics of the Navier-Stokes equations, global laws of steady and unsteady boundary layer flows and laminar and turbulent pipe flows
Engineering Fluid Mechanics
The intended purpose of this book is to provide the fundamental and physical aspects of fluid mechanics and to develop engineering practice for fluid machineries. The subject of fluid engineering is most often approached at the senior undergraduate or postgraduate level of study.
Discontinuous Galerkin Methods for Viscous Incompressible Flow
Guido Kanschat reviews several discontinuous Galerkin schemes for elliptic and viscous flow problems. Setting out from Nitsche's method for weak boundary conditions, he studies the interior penalty and LDG methods. Combined with a stable advection discretization, they yield stable DG methods for linear flow problems of Stokes and Oseen type which are applied to the Navier-Stokes problem. The author not only presents the analytical techniques used to study these methods but also devotes a major discussion to the efficient numerical solution of discrete problems.
Control of Coupled Partial Differential Equations
Contains selected contributions originating from the ‘Conference on Optimal Control of Coupled Systems of Partial Differential Equations’, held at the ‘Mathematisches Forschungsinstitut Oberwolfach’ in April 2005.
Computational Turbulent Incompressible Flow: Applied Mathematics : Body and Soul 4
This is Volume 4 of the book series of the Body & Soul mathematics education reform program, and presents a unified new approach to computational simulation of turbulent.
