Discrete Mechanics.

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-equilibrium -- 1.5.1. 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 equilibrium -- 2.8. 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 potentials -- 4.2. 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 decomposition -- 4.7. 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 -- 5.2.1. Darcian model -- 5.2.2. Stokes model -- 5.2.3. Model of an ideal fluid -- 5.2.4. Brinkman model -- 5.3. Fluid statics -- 5.3.1. Perfect gas in isothermal evolution -- 5.3.2. Perfect gas in adiabatic evolution -- 5.4. Injection of a gas into a cavity -- 5.4.1. Isothermal injection -- 5.4.2. Adiabatic injection -- 5.5. Nonlinear wave propagation -- 5.5.1. Sod shock tube -- 5.6. Thermo-acoustics -- 5.6.1. Heating of a cavity filled with air -- 5.7. Natural convection in an enclosed cavity -- 5.8. Multi-component transport -- 5.9. Modeling of phase change.

5.10. Critical opalescence -- 5.11. Conclusions regarding the multiphysics approach -- Appendix: Formulas -- A.1. Tensorial identities -- A.2. Vectorial identities -- Bibliography -- Index.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.