Solution of 3D heat conduction equations using the discontinuous Galerkin method on unstructured grids
The discontinuous Galerkin method with discontinuous basic functions which is characterized by a high order of accuracy of the obtained solution is now widely used. In this paper a new way of approximation of diffusion terms for discontinuous Galerkin method for solving diffusion-type equations is p...
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| Format: | Article |
| Language: | English |
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Samara State Technical University
2015-09-01
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| Series: | Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki |
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| Online Access: | https://journals.eco-vector.com/1991-8615/article/viewFile/20464/16711 |
| _version_ | 1818059850840539136 |
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| author | Ruslan V Zhalnin Marina E Ladonkina Victor F Masyagin Vladimir F Tishkin |
| author_facet | Ruslan V Zhalnin Marina E Ladonkina Victor F Masyagin Vladimir F Tishkin |
| author_sort | Ruslan V Zhalnin |
| collection | DOAJ |
| description | The discontinuous Galerkin method with discontinuous basic functions which is characterized by a high order of accuracy of the obtained solution is now widely used. In this paper a new way of approximation of diffusion terms for discontinuous Galerkin method for solving diffusion-type equations is proposed. The method uses piecewise polynomials that are continuous on a macroelement surrounding the nodes in the unstructured mesh but discontinuous between the macroelements. In the proposed numerical scheme the spaced grid is used. On one grid an approximation of the unknown quantity is considered, on the other is the approximation of additional variables. Additional variables are components of the heat flux. For the numerical experiment the initial-boundary problem for three-dimensional heat conduction equation is chosen. Calculations of three-dimensional modeling problems including explosive factors show a good accuracy of offered method. |
| first_indexed | 2024-12-10T13:23:05Z |
| format | Article |
| id | doaj.art-38b81f56a36f4d0e9e7b4d856b9b4cda |
| institution | Directory Open Access Journal |
| issn | 1991-8615 2310-7081 |
| language | English |
| last_indexed | 2024-12-10T13:23:05Z |
| publishDate | 2015-09-01 |
| publisher | Samara State Technical University |
| record_format | Article |
| series | Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki |
| spelling | doaj.art-38b81f56a36f4d0e9e7b4d856b9b4cda2022-12-22T01:47:16ZengSamara State Technical UniversityVestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki1991-86152310-70812015-09-0119352353310.14498/vsgtu135117884Solution of 3D heat conduction equations using the discontinuous Galerkin method on unstructured gridsRuslan V Zhalnin0Marina E Ladonkina1Victor F Masyagin2Vladimir F Tishkin3Ogarev Mordovia State UniversityKeldysh Institute of Applied Mathematics of Russian Academy of SciencesOgarev Mordovia State UniversityKeldysh Institute of Applied Mathematics of Russian Academy of SciencesThe discontinuous Galerkin method with discontinuous basic functions which is characterized by a high order of accuracy of the obtained solution is now widely used. In this paper a new way of approximation of diffusion terms for discontinuous Galerkin method for solving diffusion-type equations is proposed. The method uses piecewise polynomials that are continuous on a macroelement surrounding the nodes in the unstructured mesh but discontinuous between the macroelements. In the proposed numerical scheme the spaced grid is used. On one grid an approximation of the unknown quantity is considered, on the other is the approximation of additional variables. Additional variables are components of the heat flux. For the numerical experiment the initial-boundary problem for three-dimensional heat conduction equation is chosen. Calculations of three-dimensional modeling problems including explosive factors show a good accuracy of offered method.https://journals.eco-vector.com/1991-8615/article/viewFile/20464/16711parabolic equationsspaced gridsdiscontinuous galerkin methodconvergence and accuracy of the method |
| spellingShingle | Ruslan V Zhalnin Marina E Ladonkina Victor F Masyagin Vladimir F Tishkin Solution of 3D heat conduction equations using the discontinuous Galerkin method on unstructured grids Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki parabolic equations spaced grids discontinuous galerkin method convergence and accuracy of the method |
| title | Solution of 3D heat conduction equations using the discontinuous Galerkin method on unstructured grids |
| title_full | Solution of 3D heat conduction equations using the discontinuous Galerkin method on unstructured grids |
| title_fullStr | Solution of 3D heat conduction equations using the discontinuous Galerkin method on unstructured grids |
| title_full_unstemmed | Solution of 3D heat conduction equations using the discontinuous Galerkin method on unstructured grids |
| title_short | Solution of 3D heat conduction equations using the discontinuous Galerkin method on unstructured grids |
| title_sort | solution of 3d heat conduction equations using the discontinuous galerkin method on unstructured grids |
| topic | parabolic equations spaced grids discontinuous galerkin method convergence and accuracy of the method |
| url | https://journals.eco-vector.com/1991-8615/article/viewFile/20464/16711 |
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