Discrete mechanics / / Jean-Paul Caltagirone

• Record Nr.: UNINA9910810322803321
• Autore: Caltagirone Jean-Paul
• Pubbl/distr/stampa: London, England ; ; Hoboken, New Jersey : , : ISTE : , : Wiley, , 2015; ©2015
• ISBN: 1-119-05858-9; 1-119-05807-4; 1-119-05798-1
• Descrizione fisica: 1 online resource (253 p.)
• Collana: Fluid Mechanics Series
• Disciplina: 531.01515
• Soggetti: Mechanics, Analytic; Nonlinear mechanics
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: Cover; Title Page; Copyright; Contents; Preface; List of Symbols; Introduction; I.1. General points; I.2. Introduction; 1: Framework of Discrete Mechanics; 1.1. Frames of reference and uniform motions; 1.2. Concept of a Discrete Medium; 1.2.1. Vectors and components; 1.2.2. Physical meaning of the differential operators; 1.2.3. Use of the theorems of differential geometry; 1.2.4. Two essential properties; 1.2.5. Tensorial values; 1.2.6. The scalar and vectorial potentials; 1.3. The physical characteristics; 1.4. Equilibrium stress state; 1.4.1. Two examples of mechanical equilibrium; 1.5. Thermodynamic non-equilibrium1.5.1. Forces and fluxes; 1.6. Conservation of mass; 2: Momentum Conservation; 2.1. Classification of forces; 2.2. Three fundamental experiments; 2.2.1. Equilibrium in a glass of water; 2.2.2. Couette flow; 2.2.3. Poiseuille flow; 2.3. Postulates; 2.4. Modeling of the pressure forces; 2.5. Modeling of the viscous forces; 2.5.1. Modeling of the viscous effects of volume; 2.5.2. Modeling of the viscous surface effects; 2.5.3. Stress state; 2.6. Objectivity; 2.7. Discrete motion balance equation; 2.7.1. Fundamental law of dynamics; 2.7.2. Eulerian step; 2.7.3. Mechanical equilibrium2.8. Formulation in terms of density and temperature; 2.9. Similitude parameters; 2.9.1. Impact on the surface ; of a liquid; 2.10. Hypercompressible media; 3: Conservation of Heat Flux and Energy; 3.1. Introduction; 3.2. Conservation of flux; 3.3. Conservation of energy; 3.3.1. Conservation of total energy; 3.3.2. Conservation of kinetic energy; 3.3.3. Conservation of the internal energy; 3.4. Discrete equations for the flux and the energy; 3.5. A simple heat-conduction problem; 3.5.1. Case of anisotropic materials; 4: Properties of Discrete Equations; 4.1. A system of equations and potentials4.2. Physics represented; 4.2.1. Poiseuille flow and potentials; 4.2.2. Celerity and maximum velocity; 4.2.3. Remarks about turbulence; 4.3. Boundary conditions; 4.3.1. Contact surface; 4.3.2. Shockwaves; 4.3.3. Edge conditions; 4.3.4. Slip condition; 4.3.5. Capillary effects; 4.3.6. Thermal boundary conditions; 4.4. Penalization of the potentials; 4.5. Continua and discrete mediums; 4.5.1. Differences with the Navier-Stokes equation; 4.5.2. Dissipation; 4.5.3. Case of rigidifying motions; 4.5.4. An example of the dissipation of energy; 4.6. Hodge-Helmholtz decomposition4.7. Approximations; 4.7.1. Bernoulli's law; 4.7.2. Irrotational flow; 4.7.3. Inviscid fluid; 4.7.4. Incompressible flow; 4.8. Gravitational waves; 4.9. Linear visco-elasticity; 4.9.1. Viscous dissipation in a visco-elastic medium; 4.9.2. Dissipation of longitudinal waves in a visco-elastic medium; 4.9.3. Consistency with Continuum Mechanics; 4.9.4. Pure compression; 4.9.5. Pure shear stress; 4.9.6. Bingham fluid; 5: Multiphysics; 5.1. Extensions to other branches of physics; 5.1.1. Coupling between a fluid and a porous medium; 5.2. Flow around a cylinder in an infinite medium
• Sommario/riassunto: This book presents the fundamental principles of mechanics to re-establish the equations of Discrete Mechanics. It introduces physics and thermodynamics associated to the physical modeling. The development and the complementarity of sciences lead to review today the old concepts that were the basis for the development of continuum mechanics. The differential geometry is used to review the conservation laws of mechanics. For instance, this formalism requires a different location of vector and scalar quantities in space. The equations of Discrete Mechanics form a system of equations where the H