A brief overview of modern research of the processes dynamics in unsteady water ows using the shallow water equation
In hydrodynamics (hydraulics), there are numerous approaches to solving the problem of water flow dynamics control in river beds and channels, while the results of each methods differ, and estimates of their reliability do not always exist. The shallow water equation (or Saint-Venant's equation...
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| Format: | Article |
| Language: | English |
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Al-Farabi Kazakh National University
2021-12-01
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| Series: | Вестник КазНУ. Серия математика, механика, информатика |
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| Online Access: | https://bm.kaznu.kz/index.php/kaznu/article/view/972/641 |
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| author | Abdumaulen Suleymanovich Berdyshev Zhanars Alda-ongarovich Abduramanov Dana Nazarbaevna Bliyeva Nazgul Smilkhanovna Akhtayeva |
| author_facet | Abdumaulen Suleymanovich Berdyshev Zhanars Alda-ongarovich Abduramanov Dana Nazarbaevna Bliyeva Nazgul Smilkhanovna Akhtayeva |
| author_sort | Abdumaulen Suleymanovich Berdyshev |
| collection | DOAJ |
| description | In hydrodynamics (hydraulics), there are numerous approaches to solving the problem of water flow dynamics control in river beds and channels, while the results of each methods differ, and estimates of their reliability do not always exist. The shallow water equation (or Saint-Venant's equations in one-dimensional form) is often used by hydraulic engineers in their practice. Its apparent simplicity and ability to describe well enough the behavior of rivers and flows make it a useful tool for many applications, such as the regulation of navigable rivers and irrigation networks in agriculture. The main direction of research in the field of numeric problems described by Saint-Venant equations is the development of numerical methods of computation implemented on super-powerful computers. Development of numerical models of surface water dynamics in the shallow water approximation is actively advancing during the recent years.
The article is devoted to a review of mathematical studies of the dynamics of processes in unsteady water flows using differential equations, as well as an assessment of these approaches from the point of view of the model's reflection of real processes.
The work is aimed at analyzing different approaches to modeling the dynamics of processes in non-stationary water flows. The objectives of the study include the analysis of scientific publications with different approaches to modeling the shallow water equation, taking into account factors, parameters, and modeling methods. |
| first_indexed | 2024-04-10T19:36:00Z |
| format | Article |
| id | doaj.art-d7723f15f6ca4e309f4e63d554641cd1 |
| institution | Directory Open Access Journal |
| issn | 1563-0277 2617-4871 |
| language | English |
| last_indexed | 2024-04-10T19:36:00Z |
| publishDate | 2021-12-01 |
| publisher | Al-Farabi Kazakh National University |
| record_format | Article |
| series | Вестник КазНУ. Серия математика, механика, информатика |
| spelling | doaj.art-d7723f15f6ca4e309f4e63d554641cd12023-01-30T06:18:14ZengAl-Farabi Kazakh National UniversityВестник КазНУ. Серия математика, механика, информатика1563-02772617-48712021-12-011124170180https://doi.org/10.26577/JMMCS.2021.v112.i4.15A brief overview of modern research of the processes dynamics in unsteady water ows using the shallow water equationAbdumaulen Suleymanovich Berdyshev0https://orcid.org/0000-0002-1228-8246Zhanars Alda-ongarovich Abduramanov1https://orcid.org/0000-0003-3820-7253Dana Nazarbaevna Bliyeva2https://orcid.org/0000-0001-7703-0329Nazgul Smilkhanovna Akhtayeva3https://orcid.org/0000-0002-0835-9814Abay Kazakh National Pedagogical University, Institute of Information and Computational Technologies, Kazakhstan, AlmatyAbay Kazakh National Pedagogical University, Institute of Information and Computational Technologies, Kazakhstan, AlmatyInstitute of Information and Computational Technologies, Kazakhstan, AlmatyInstitute of Information and Computational Technologies, Kazakhstan, AlmatyIn hydrodynamics (hydraulics), there are numerous approaches to solving the problem of water flow dynamics control in river beds and channels, while the results of each methods differ, and estimates of their reliability do not always exist. The shallow water equation (or Saint-Venant's equations in one-dimensional form) is often used by hydraulic engineers in their practice. Its apparent simplicity and ability to describe well enough the behavior of rivers and flows make it a useful tool for many applications, such as the regulation of navigable rivers and irrigation networks in agriculture. The main direction of research in the field of numeric problems described by Saint-Venant equations is the development of numerical methods of computation implemented on super-powerful computers. Development of numerical models of surface water dynamics in the shallow water approximation is actively advancing during the recent years. The article is devoted to a review of mathematical studies of the dynamics of processes in unsteady water flows using differential equations, as well as an assessment of these approaches from the point of view of the model's reflection of real processes. The work is aimed at analyzing different approaches to modeling the dynamics of processes in non-stationary water flows. The objectives of the study include the analysis of scientific publications with different approaches to modeling the shallow water equation, taking into account factors, parameters, and modeling methods.https://bm.kaznu.kz/index.php/kaznu/article/view/972/641saint-venant equationsdynamics of unsteady river currentsnumerical methodsa system of hyperbolic differential equationshigh-performance computing |
| spellingShingle | Abdumaulen Suleymanovich Berdyshev Zhanars Alda-ongarovich Abduramanov Dana Nazarbaevna Bliyeva Nazgul Smilkhanovna Akhtayeva A brief overview of modern research of the processes dynamics in unsteady water ows using the shallow water equation Вестник КазНУ. Серия математика, механика, информатика saint-venant equations dynamics of unsteady river currents numerical methods a system of hyperbolic differential equations high-performance computing |
| title | A brief overview of modern research of the processes dynamics in unsteady water ows using the shallow water equation |
| title_full | A brief overview of modern research of the processes dynamics in unsteady water ows using the shallow water equation |
| title_fullStr | A brief overview of modern research of the processes dynamics in unsteady water ows using the shallow water equation |
| title_full_unstemmed | A brief overview of modern research of the processes dynamics in unsteady water ows using the shallow water equation |
| title_short | A brief overview of modern research of the processes dynamics in unsteady water ows using the shallow water equation |
| title_sort | brief overview of modern research of the processes dynamics in unsteady water ows using the shallow water equation |
| topic | saint-venant equations dynamics of unsteady river currents numerical methods a system of hyperbolic differential equations high-performance computing |
| url | https://bm.kaznu.kz/index.php/kaznu/article/view/972/641 |
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