Computational Methods for Flow and Transport in Porous Media by R. Eymard, R. Herbin, D. Hilhorst, N. Ramarosy (auth.), J.

By R. Eymard, R. Herbin, D. Hilhorst, N. Ramarosy (auth.), J. M. Crolet (eds.)

The first Symposium on fresh Advances in difficulties of circulation and delivery in Porous Media used to be held in Marrakech in June '96 and has supplied a spotlight for the usage of laptop tools for fixing the numerous advanced difficulties encountered within the box of solute shipping in porous media. This symposium has been winning in bringing jointly scientists, physicists, hydrogeologists, researchers in soil and fluid mechanics and engineers serious about this multidisciplinary topic. it's transparent that the usage of computer-based versions during this area continues to be quickly increasing and that new and novel suggestions are being built. The contributed papers which shape this publication mirror the new advances, specifically with admire to new tools, inverse difficulties, reactive shipping, unsaturated media and upscaling. those were subdivided into the next sections: I. Numerical tools II. Mass delivery and warmth move III. comparability with experimentation and simulation of genuine situations This ebook includes reviewed articles of the head shows held through the overseas Symposium on laptop tools in Porous Media Engineering which happened in Giens (France) in October 1998. all the displays and the optimism proven in the course of the assembly supplied additional proof that machine modeling is making awesome development and is certainly changing into a vital toolkit within the box of porous media and solute delivery. i think that the content material of this publication presents facts of this and moreover offers a entire overview of the theoretical advancements and applications.

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2. FORCHHEIMER'S ANALYSIS In two articles on the non-linear-deviations to Darcy's law, [3] proposes three ad hoc formulae -'\lp = G'v+f3v 2 , where G' is the ratio of the pressure drop (measured in height of water) to the thickness of the sand bed and v is the seepage velocity (measured in meters per day). Here, we emphasize that although Forchheimer's analysis may be of some engineering value, no physical conclusion can reasonably be drawn from it by comparing the relative value of coefficients G', (3, and I, for it uses the dimensionalized quantity v.

0. " '·"·""·'30'·"·""·"·"·'·' ....... " . _' . _. _..... 1 o O~~__~__+-~~O~~~__-+~ o 20 40 60 Figure 5. 3. 3() IS 18 20 Figure 6. 22 2- 0 0 3 12 Time dependence of the angle a For strongly inertial flows, we study the transition to unsteady periodic solutions. The values of the critical Reynolds number depend on the angle () that the incoming flow makes with the x-axis. The critical Reynolds number increases with the angle of the flow. Figure 6 deals with the transition INERTIAL FLOW ANISOTROPY IN OBLIQUE FLOW ..

In the first intermediate time step a velocity field V* = (u*, v*) is computed by making implicit the viscous and penalty terms, whereas the convective term and the pressure gradient are made explicit. In order to obtain a good prediction in time, a discretization which is formally precise at the second order was used for viscous and convective terms. The provisional value of the horizontal component of the velocity u* is computed by : INERTIAL FLOW ANISOTROPY IN OBLIQUE FLOW... 31 This penalization technique has been introduced by [4]; it is more or less similar to the fictitious domain methods.

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