## Discrete MechanicsThis 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 Helmholtz-Hodge decomposition plays an important role. |

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### Contents

FRAMEWORK OF DISCRETE MECHANICS | 1 |

MOMENTUM CONSERVATION | 33 |

CONSERVATION OF HEAT FLUX | 91 |

PROPERTIES OF DISCRETE EQUATIONS | 105 |

MULTIPHYSICS | 165 |

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### Common terms and phrases

acceleration accumulation basis behavior boundary conditions calculated cavity celerity of sound components compressibility coefficient conservation equation conservation law conservation of mass considered constant Continuum Mechanics corresponds defined density direction Discrete Mechanics displacement dissipation divergence domain dual topology dual volume edge enables equal evolution expressed Figure flow fluid forces of pressure formulation frame of reference function gradient gravity heat flux Hodge–Helmholtz decomposition incompressible integration interface introduced isothermal law of dynamics linear linked material derivative mechanical equilibrium motion balance equation Navier–Stokes equation Newtonian fluid null obtained orthogonal perfect gas phenomena physical Poiseuille flow porous medium primal surface primal topology propagation properties relation represented rotational stress scalar potential shear stress shockwave solid solution Stokes system of equations temperature theorem thermal thermodynamic transversal waves unit vector values variables variation vector potential vectorial equation velocity viscous effects waves written