Construction of approximate solutions to the riemann problem for two-phase flow of immiscible liquids by modifying the vanishing viscosity method

Authors

DOI:

https://doi.org/10.15587/1729-4061.2022.258098

Keywords:

pressure-dependent viscosity, Buckley-Leverett model, Riemann problem

Abstract

In the paper, we apply the vanishing viscosity method for an approximate solution to the Riemann problem. This approach gives the effects of the accuracy of the solution and the speed of convergence by discrediting time and spatial variables.

The obtained method ensures the smoothness of the solution without taking into account the capillary pressure. The results confirm the negligible influence of cross-link conditions compared to the classical Darcy approach.

The proposed solutions of the new approach are intended to improve the methods and schemes of discretization both in space and in time. This is achieved by minimizing viscosity, and discretization in space and time. These factors are of paramount importance for studying phenomena with variable saturation in the transient mode and analyzing water/oil flows and migrations in real time, since discretization in space and time affects the accuracy and convergence of calculations. Our result in the form of obtaining viscous solutions of the filtration process is interesting from a theoretical point of view. From a practical point of view, numerical modeling allows early prediction of performance. Thus, the applied aspect of using the obtained scientific result is the possibility of improving the process by taking into account the influence of phases of fluid flows

Author Biographies

Yerbol Aldanov, Astana International University

Candidate of Physical and Mathematical Sciences, Associate Professor

Higher School of Information Technology and Engineering

Timur Toleuov, K. Zhubanov Aktobe Regional University

Doctoral Student

Department of Mathematics

Nurbolat Tasbolatuly, Astana International University

PhD, Associate Professor

Higher School of Information Technology and Engineering

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Published

2022-06-30

How to Cite

Aldanov, Y., Toleuov, T., & Tasbolatuly, N. (2022). Construction of approximate solutions to the riemann problem for two-phase flow of immiscible liquids by modifying the vanishing viscosity method . Eastern-European Journal of Enterprise Technologies, 3(4 (117), 40–48. https://doi.org/10.15587/1729-4061.2022.258098

Issue

Vol. 3 No. 4 (117) (2022): Mathematics and Cybernetics - applied aspects

Section

Mathematics and Cybernetics - applied aspects

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Copyright (c) 2022 Yerbol Aldanov, Timur Toleuov, Nurbolat Tasbolatuly

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