A stationary principle for non conservative systems |
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| Authors: | Shaul Sorek |
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| Institution: | Department of Hydrology and Water Resources, University of Arizona, Tucson, AZ 85721, USA |
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| Abstract: | A stationary principle is described to yield governing integral formulations for dissipative systems. Variation is applied on selective terms of energy or momentum functionals resulting with force or mass balance equations respectively. Applying the principle for a motion of a viscous fluid yields the Navier-Stokes equations as an approximation of the functional (i.e. equating to zero part of the integrand). When a Darcy's flow regime in a porous media is considered, implementing a space averaging method on the resultant integral derived by the principle, Forchheimer's law for energy accumulation and solute transport equation for momentum assembling are yielded in differential form approximation of a more extended functional formulation. |
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| Keywords: | Hamilton's extended principle dissipative systems energy momentum Darcy flow regime spatial averaging minimum criterion |
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