Development of parallel implementation for the Navier-Stokes equation in doubly connected areas using the fictitious domain method

Authors

DOI:

https://doi.org/10.15587/1729-4061.2022.254261

Keywords:

Navier-Stokes equations, stream function, vorticity, numerical methods, parallel algorithm

Abstract

This paper presents a numerical realization of the Navier-Stokes equations in irregular domains using the fictitious domain method with a continuation along with the lowest coefficient. To solve numerous connected issues in irregular regions, the fictitious domain method is broadly used. The advantage of the fictitious domain method is that the problem is solved not in the original complex domain, but in a few other, easier domains. Using the method, computation is done easily for a sufficiently wide class of problems with arbitrary computational domains.

The problem is solved using two methods. The primary method is based on the development of a distinct issue in variables of the stream function and the vortex velocity using the pressure uniqueness condition. The second method is to understand the expressed issue by the fictitious domain method with a continuation by lower coefficients.

Using the fictitious domain method, a computational algorithm is constructed based on the explicit finite difference schemes. The finite difference scheme is stable and has high computational accuracy and it gives the possibility to parallelize. Temperature distributions and stream functions are presented as numerical results.

A parallel algorithm has been developed using Open Multi-Processing (hereinafter OpenMP) and Message Passing Interface (hereinafter MPI) technologies. Within the parallel approach, we used OpenMP technology for parallel calculation of vorticity and stream work, and for calculating temperature we applied MPI technology. The performance analysis on our parallel code shows favorable strong and weak scalability. The test results show that the code running in the parallel approach gives the expected results by comparing our results with those obtained while running the same simulation on the central processing unit (CPU)

Supporting Agency

  • This research is funded by the Science Committee of the Ministry of Education and Science of the Republic of Kazakhstan (Grant No. AP09058430).

Author Biographies

Almas Temirbekov, Al-Farabi Kazakh National University

PhD, Associate Professor

Department of Computational Sciences and Statistics

Arshyn Altybay, Al-Farabi Kazakh National University

PhD, Senior Lecturer

Department of Computer Science

Laura Temirbekovа, Abai Kazakh National Pedagogical University

PhD, Senior Lecturer

Department of Informatics and Informatization of Education

Syrym Kasenov, Al-Farabi Kazakh National University

PhD, Senior Lecturer

Department of Computational Sciences and Statistics

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Published

2022-04-28

How to Cite

Temirbekov, A., Altybay, A., Temirbekovа L., & Kasenov, S. (2022). Development of parallel implementation for the Navier-Stokes equation in doubly connected areas using the fictitious domain method . Eastern-European Journal of Enterprise Technologies, 2(4 (116), 38–46. https://doi.org/10.15587/1729-4061.2022.254261

Issue

Vol. 2 No. 4 (116) (2022): Mathematics and Cybernetics - applied aspects

Section

Mathematics and Cybernetics - applied aspects

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Copyright (c) 2022 Almas Temirbekov, Arshyn Altybay, Laura Temirbekovа, Syrym Kasenov

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