MSC2010 34C20
Construction of a parallel computational algorithm based on the Galerkin discontinuous method for solving convective heat transfer problems on unstructured staggered grids
R. V. Zhalnin1, V. F. Masyagin2, E. E. Peskova3
| Annotation | The present paper is devoted to the construction of a parallel computational algorithm for solving convective heat transfer problems using the discontinuous Galerkin method on unstructured staggered grids. The computational algorithm is implemented on the basis of MPI parallel computing technology. A special feature of the algorithm is that auxiliary variables that occur when the diffusion terms are approximated by the discontinuous Galerkin method are not involved in interprocessor exchange. The developed parallel algorithm is applied to modelling of temperature dynamics in formation with a vertical injection well and hydraulic fracturing. The paper presents the results of a computational experiment and estimates the effectiveness of a parallel algorithm. |
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| Keywords | discontinuous Galerkin method, vertical injection well, hydraulic fracturing, convective heat transfer equation, staggered grids, parallel computing, MPI technology |
1Ruslan V. Zhalnin, Head of Department of Applied Mathematics, Differential Equations and Theoretical Mechanics, National Research Mordovia State University (68/1 Bolshevistskaya St., Saransk 430005, Russia), Ph.D. (Physics and Mathematics), ORCID: http://orcid.org/0000-0002-1103-3321, zhrv@mrsu.ru
2Viktor F. Masyagin, Senior Researcher, National Research Mordovia State University (68/1 Bolshevistskaya St., Saransk 430005, Russia), Ph.D. (Physics and Mathematics), ORCID: http://orcid.org/0000-0001-6738-8183, vmasyagin@gmail.com
3Elizaveta E. Peskova, Junior Researcher, National Research Mordovia State University (68/1 Bolshevistskaya St., Saransk 430005, Russia), ORCID: http://orcid.org/0000-0003-2618-1674, e.e.peskova@mail.ru
Citation: R. V. Zhalnin, V. F. Masyagin, E. E. Peskova, "[Construction of a parallel computational algorithm based on the Galerkin discontinuous method for solving convective heat transfer problems on unstructured staggered grids]", Zhurnal Srednevolzhskogo matematicheskogo obshchestva,20:4 (2018) 448–459 (In Russian)
DOI 10.15507/2079-6900.20.201804.448-459
