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One-dimensional unsteady inertial flow in phreatic aquifers induced by a sudden change of the boundary head 总被引:2,自引:0,他引:2
Konstadinos N. Moutsopoulos 《Transport in Porous Media》2007,70(1):97-125
We are examining the classical problem of unsteady flow in a phreatic semi-infinite aquifer, induced by sudden rise or drawdown
of the boundary head, by taking into account the influence of the inertial effects. We demonstrate that for short times the
inertial effects are dominant and the equation system describing the flow behavior can be reduced to a single ordinary differential
equation. This equation is solved both numerically by the Runge-Kutta method and analytically by the Adomian’s decomposition
approach and an adequate polynomial-exponential approximation as well. The influence of the viscous term, occurring for longer
times, is also taken into account by solving the full Forchheimer equation by a finite difference approach. It is also demonstrated
that as for the Darcian flow, for the case of small fluctuations of the water table, the computation procedure can be simplified
by using a linearized form of the mass balance equation. Compact analytical expressions for the computation of the water stored
or extracted from an aquifer, including viscous corrections are also developed. 相似文献
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Nicholas John Moutsopoulos 《Speculations in Science and Technology》1998,21(3):161-169
We express the masses of elementary particles as simple polynomials of (=3.14...). The calculated masses differ only slightly from the experimentally found ones and, in most cases, are within the error margins accepted in the experiments. This method of calculation is part of our work titled The pionic theory of matter. 相似文献
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Konstantinos N. Moutsopoulos 《Transport in Porous Media》2010,85(3):919-940
The classical problem of flow induced by a sudden change of the piezometic head in a semi-infinite aquifer is re-examined.
A new analytical solution is derived, by combining an expression describing the water table elevation upstream, obtained by
the Adomian’s decomposition approach, to an existing polynomial expression (Tolikas et al. in Water Resour Res 20:24–28, 1984),
adequate for the downstream region; the parameters of both approximations are computed by matching the two solutions at the
inflection point of the water table. Although several analytical solutions are available in the literature, we demonstrate
that the expression we have developed in this issue is the most accurate for strong or moderate non-linear flows, where the
degree of non-linearity is defined as the ratio of the piezometric head elevation at the origin to the initial water table
elevation. For this type of flows the perturbation-series solution of Polubarinova-Kochina, characterized by previous studies
as the best available analytical solution provides physically unacceptable results, while the analytical solution of Lockington
(J Irrig Drain Eng 123:24–27, 1997), used to check the accuracy of numerical schemes, underestimates the penetration distance
of the recharging front. 相似文献
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Using a Kaluza-Klein dimensional reduction, and further imposing a conformal Killing symmetry on the reduced metric generated
by the dilaton, we show an Ansatz that yields many of the known stationary axisymmetric solutions to TMG. 相似文献
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