05308nam 2200649 450 991081032280332120200520144314.01-119-05858-91-119-05807-41-119-05798-1(CKB)3710000000315823(EBL)1890998(SSID)ssj0001432365(PQKBManifestationID)11852772(PQKBTitleCode)TC0001432365(PQKBWorkID)11388889(PQKB)11095169(MiAaPQ)EBC1890998(Au-PeEL)EBL1890998(CaPaEBR)ebr10997825(OCoLC)898213751(EXLCZ)99371000000031582320150106h20152015 uy 0engur|n|---|||||txtccrDiscrete mechanics /Jean-Paul CaltagironeLondon, England ;Hoboken, New Jersey :ISTE :Wiley,2015.©20151 online resource (253 p.)Fluid Mechanics SeriesDescription based upon print version of record.1-84821-678-5 Includes bibliographical references and index.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 equilibrium1.5. 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 step2.7.3. 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 Equations4.1. 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 energy4.6. 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 medium5.2. Flow around a cylinder in an infinite mediumThis 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 HFluid mechanics series.Mechanics, AnalyticNonlinear mechanicsMechanics, Analytic.Nonlinear mechanics.531.01515Caltagirone Jean-Paul895423MiAaPQMiAaPQMiAaPQBOOK9910810322803321Discrete mechanics4035975UNINA