Mathematical modeling of two-phase compressible fluid filtration based on modified adaptive method of minimum amendments
| Autor: | Andrey A. Sukhinov, Lusine A. Grigoryan, A. I. Sukhinov |
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| Rok vydání: | 2016 |
| Předmět: |
non-selfadjoint operator
Adaptive method two-phase compressible fluid filtration problems finite-difference equations задачи фильтрации двухфазных сжимаемых жидкостей Mechanics Compressible flow law.invention адаптивный метод минимальных поправок law сеточные уравнения Management of Technology and Innovation Phase (matter) TA401-492 несамосопряженный оператор adaptive method of minimum amendments Materials of engineering and construction. Mechanics of materials Filtration Mathematics |
| Zdroj: | Advanced Engineering Research, Vol 16, Iss 3, Pp 96-109 (2016) |
| ISSN: | 1992-5980 |
| DOI: | 10.12737/20944 |
| Popis: | The work objective is to build and investigate the modified adaptive method of minimum amendments (MAMMA) which is destined for the numerical simulation of the two-phase compressible fluid filtration in porous media. This approach allows overcoming the known use limitations of other methods of the finite-difference equations solution, such as: crucial differential pressures acting on the oil-and-water bearing formation; and the compressibility of the medium at the considerable gas content in the oil phase. An approximation method - an explicit one for defining the function of water saturation, and an implicit one for the pressure function computation - is selected as the research basis. When setting the initial boundary value problem and its sampling, the process of the two-phase compressible fluid filtration in the space-dimensional domain with the lateral area bounded below by the subface of stratum, and above - by the bed top, is considered. A two-layer iterative method of the variational type - a modified method of minimal amendments adapted for solving finite-difference equations of the two-phase compressible fluid with a non-selfadjoint operator under the most general assumptions on the properties of the grid-problem operator is built. It is shown that a MAMMA has the asymptotic convergence rate characteristic of the “classical” alternate triangular method that does not use the Chebyshev acceleration technique and can be applied to the problems with a self-adjoint operator. Numerical experiments have confirmed the high efficiency of MAMMA. It is established that to achieve the specified accuracy, the number of iterations at the MAMMA reduces to 3-20 times as compared to the method of Seidel and the overrelaxation method. |
| Databáze: | OpenAIRE |
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