Novosibirsk, Russia, May, 30 – June, 4, 2011

International Conference
"Modern Problems of Applied Mathematics and Mechanics: Theory, Experiment and Applications", devoted to the 90th anniversary of professor Nikolai N. Yanenko

Emikh V.  

Theoretical analysis and computation technologies in filtration problems

The greater attention is given in last decades for filtration flows researches of fluids with various physical properties. Mathematical models of such fluids are before unstudied multiparameteric boundary-value problems of the analytical function theory. The solution of problems requires a deep theoretical analysis in conjunction with spacious and sometimes highly laborious computational operations. By such approach the complex of models of two-dimensional filtration flows with mobile boundaries was been created.
The central position in this complex occupied the problems of filtration towards horizontal drains in a fresh water fringe above salt ground waters. Specific of such flows is associated with the presence of two unknown mobile boundaries under influence of drainage. His intensity is submitted to restrictions established by the computations critical regimes of drainage.
By analysis of filtration flows in direct statement the finding of unknown conformal mapping parameters problem is appeared. Iteration cyclical procedures fulfilled by special computer programs are used for solution of transcendental equations system binding unknown parameters with physical parameters governing over flow. All singularities in integrals that contain in computation formulas are eliminated preliminary, the solubility of equations relatively to mapping parameters is established.
Also the problems of oil flow towards horizontal screens in layers containing liquids with different physical properties or gas are included into the complex of stratified seepage flows models. The primary attention is paid to pumping regimes with maximum of oil extraction without dashes. Approach to calculation of inaccessible for measuring volumes of these liquids was been elaborated using of analytical rations received when solving of boundary-value problems.

Abstracts file: ЯНЕНКО.DOC
Full text file: Emikh.pdf

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