An Efficient Parallel Implementation of the Runge–Kutta Discontinuous Galerkin Method with Weighted Essentially Non-Oscillatory Limiters on Three-Dimensional Unstructured Meshes
In computational fluid dynamics, high-order solvers suitable for three-dimensional unstructured meshes are attractive but are less developed than other methods. In this article, we provide the formulation and a parallel implementation of the Runge–Kutta discontinuous Galerkin finite element method w...
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| Format: | Article |
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MDPI AG
2022-04-01
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| Series: | Applied Sciences |
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| Online Access: | https://www.mdpi.com/2076-3417/12/9/4228 |
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| author | Weicheng Pei Yuyan Jiang Shu Li |
| author_facet | Weicheng Pei Yuyan Jiang Shu Li |
| author_sort | Weicheng Pei |
| collection | DOAJ |
| description | In computational fluid dynamics, high-order solvers suitable for three-dimensional unstructured meshes are attractive but are less developed than other methods. In this article, we provide the formulation and a parallel implementation of the Runge–Kutta discontinuous Galerkin finite element method with weighted essentially non-oscillatory limiters, which are compact and effective for suppressing numerical oscillations near discontinuities. In our experiments, high-order solvers do outperform their low-order counterparts in accuracy and the efficient parallel implementation makes the time cost affordable for large problems. Such high-order parallel solvers are efficient tools for solving conservative laws including the Euler system that models inviscid compressible flows. |
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| format | Article |
| id | doaj.art-136059b83cdb4d80b3ea077d0ccddf66 |
| institution | Directory Open Access Journal |
| issn | 2076-3417 |
| language | English |
| last_indexed | 2024-03-10T04:22:33Z |
| publishDate | 2022-04-01 |
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| spelling | doaj.art-136059b83cdb4d80b3ea077d0ccddf662023-11-23T07:46:05ZengMDPI AGApplied Sciences2076-34172022-04-01129422810.3390/app12094228An Efficient Parallel Implementation of the Runge–Kutta Discontinuous Galerkin Method with Weighted Essentially Non-Oscillatory Limiters on Three-Dimensional Unstructured MeshesWeicheng Pei0Yuyan Jiang1Shu Li2School of Aeronautics Science and Engineering, Beihang University, 37 Xueyuan Road, Haidian District, Beijing 100191, ChinaSchool of Aeronautics Science and Engineering, Beihang University, 37 Xueyuan Road, Haidian District, Beijing 100191, ChinaSchool of Aeronautics Science and Engineering, Beihang University, 37 Xueyuan Road, Haidian District, Beijing 100191, ChinaIn computational fluid dynamics, high-order solvers suitable for three-dimensional unstructured meshes are attractive but are less developed than other methods. In this article, we provide the formulation and a parallel implementation of the Runge–Kutta discontinuous Galerkin finite element method with weighted essentially non-oscillatory limiters, which are compact and effective for suppressing numerical oscillations near discontinuities. In our experiments, high-order solvers do outperform their low-order counterparts in accuracy and the efficient parallel implementation makes the time cost affordable for large problems. Such high-order parallel solvers are efficient tools for solving conservative laws including the Euler system that models inviscid compressible flows.https://www.mdpi.com/2076-3417/12/9/4228high-order CFD solversdiscontinuous Galerkin methodsWENO limitersthree-dimensional unstructured meshesdistributed memory parallelization |
| spellingShingle | Weicheng Pei Yuyan Jiang Shu Li An Efficient Parallel Implementation of the Runge–Kutta Discontinuous Galerkin Method with Weighted Essentially Non-Oscillatory Limiters on Three-Dimensional Unstructured Meshes Applied Sciences high-order CFD solvers discontinuous Galerkin methods WENO limiters three-dimensional unstructured meshes distributed memory parallelization |
| title | An Efficient Parallel Implementation of the Runge–Kutta Discontinuous Galerkin Method with Weighted Essentially Non-Oscillatory Limiters on Three-Dimensional Unstructured Meshes |
| title_full | An Efficient Parallel Implementation of the Runge–Kutta Discontinuous Galerkin Method with Weighted Essentially Non-Oscillatory Limiters on Three-Dimensional Unstructured Meshes |
| title_fullStr | An Efficient Parallel Implementation of the Runge–Kutta Discontinuous Galerkin Method with Weighted Essentially Non-Oscillatory Limiters on Three-Dimensional Unstructured Meshes |
| title_full_unstemmed | An Efficient Parallel Implementation of the Runge–Kutta Discontinuous Galerkin Method with Weighted Essentially Non-Oscillatory Limiters on Three-Dimensional Unstructured Meshes |
| title_short | An Efficient Parallel Implementation of the Runge–Kutta Discontinuous Galerkin Method with Weighted Essentially Non-Oscillatory Limiters on Three-Dimensional Unstructured Meshes |
| title_sort | efficient parallel implementation of the runge kutta discontinuous galerkin method with weighted essentially non oscillatory limiters on three dimensional unstructured meshes |
| topic | high-order CFD solvers discontinuous Galerkin methods WENO limiters three-dimensional unstructured meshes distributed memory parallelization |
| url | https://www.mdpi.com/2076-3417/12/9/4228 |
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