Dinara A. Omariyeva

Dissertation topic

Numerical methods for solving the nonequilibrium filtration model of a two-phase incompressible fluid

Domestic scientific consultant

Nurlan M. Temirbekov, Doctor of Ph. D., Professor, Academician of the National Academy of Sciences of the Republic of Kazakhstan. The Hirsch index: 3 (according to the scopus database). Almaty, Vice-President of the National Engineering Academy of the Republic of Kazakhstan.

Scopus Author ID: https://www.scopus.com/authid/detail.uri?authorId=6506592930.

Foreign scientific consultant

Gayaz S. Khakimzyanov, Doctor of Ph. D., Professor. The Hirsch index (Web of Science): 8 (according to the scopus database). Russia, Novosibirsk, Leading Researcher at the Institute of Computing Technologies SB RAS.

Scopus Author ID: https://www.scopus.com/authid/detail.uri?authorId=6603081316.

Main scientific results

1. A new formulation of the problem of two-phase nonequilibrium filtration of an incompressible fluid using the concept of global pressure is obtained.

2. A hybrid finite element method for solving the problem is developed. A theorem on the existence of a unique sequence of approximate solutions is proved. The theorem on the convergence of the constructed method with the second order with respect to the spatial and temporal variables is proved.

3. An iterative method for solving the equation for pressure and a stabilized method for solving the equation for saturation are constructed.

Direct result

1. The software implementation of the constructed finite element method is carried out, its a posteriori analysis is carried out on the basis of computational experiments.

2. A comparative error analysis was performed using four types of mesh (including thickening along the gap line and near the gap at the boundary).

Scientific works

Articles in KKSON:

  • Н.М.Темирбеков, Д.Р.Байгереев, Д.А.Омариева «Применение стабилизированного метода бисопряженных градиентов для решения уравнения для давления в задаче двухфазной неравновесной фильтрации». Вестник КазНИТУ, октябрь 2019 г., №5 (135), стр.663-669.
  • Д.Р. Байгереев, Н.М. Темирбеков, Д.А. Омариева «Построение итерационного метода решения нелинейного уравнения эллиптического типа на основе смешанного метода конечных элементов». Вестник КазНУ, 2020 г., №2(106), стр.104-120.
  • DOI: https://doi.org/10.26577/JMMCS.2020.v106.i2.09.

The Hirsch index

1. Project with grant funding of the Committee of Science of the Ministry of Education and Science of the Republic of Kazakhstan for 2020-2022 on the topic «Development and research of parallel finite element methods for solving nonlinear multiphase filtration problems» АР08053189, project manager D.R. Baigereyev.

2. Project with grant funding of the Committee of Science of the Ministry of Education and Science of the Republic of Kazakhstan for 2020-2022 on the «Development of a module of the geoinformation system based on the methods of intelligent detection of anomalies for deep field surveys» AP08856012, project manager N.M. Temirbekov.

Funded research projects

-

Level of foreign language proficiency

-