A Compact Gas-Kinetic Scheme with Scalable Geometric Multigrid Acceleration for Steady-State Computation on 3D Unstructured Meshes
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arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910317851705344 |
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| author | Liu, Hongyu Ji, Xing Mao, Yunpeng Ding, Yuan Xu, Kun |
| author_facet | Liu, Hongyu Ji, Xing Mao, Yunpeng Ding, Yuan Xu, Kun |
| contents | In this paper, we present an advanced high-order compact gas-kinetic scheme (CGKS) for 3D unstructured mixed-element meshes, augmented with a geometric multigrid technique to accelerate steady-state convergence. The scheme evolves cell-averaged flow variables and their gradients on the original mesh. Mesh coarsening employs a two-step parallel agglomeration algorithm using a random hash for cell interface selection and a geometric skewness metric for deletion confirmation, ensuring both efficiency and robustness. For the coarser meshes, first-order kinetic flux vector splitting (KFVS) schemes with explicit or implicit time-stepping are used. The proposed multigrid CGKS is tested across various flow regimes on hybrid unstructured meshes, demonstrating significant improvements. A three-layer V-cycle multigrid strategy, coupled with an explicit forward Euler method on coarser levels, results in a convergence rate up to ten times faster than standard CGKS. In contrast, the implicit lower-upper symmetric Gauss-Seidel (LU-SGS) method offers limited convergence acceleration. Our findings indicate that the explicit multigrid CGKS is highly scalable and effective for large-scale computations, marking a substantial step forward in computational fluid dynamics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_02075 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Compact Gas-Kinetic Scheme with Scalable Geometric Multigrid Acceleration for Steady-State Computation on 3D Unstructured Meshes Liu, Hongyu Ji, Xing Mao, Yunpeng Ding, Yuan Xu, Kun Computational Physics In this paper, we present an advanced high-order compact gas-kinetic scheme (CGKS) for 3D unstructured mixed-element meshes, augmented with a geometric multigrid technique to accelerate steady-state convergence. The scheme evolves cell-averaged flow variables and their gradients on the original mesh. Mesh coarsening employs a two-step parallel agglomeration algorithm using a random hash for cell interface selection and a geometric skewness metric for deletion confirmation, ensuring both efficiency and robustness. For the coarser meshes, first-order kinetic flux vector splitting (KFVS) schemes with explicit or implicit time-stepping are used. The proposed multigrid CGKS is tested across various flow regimes on hybrid unstructured meshes, demonstrating significant improvements. A three-layer V-cycle multigrid strategy, coupled with an explicit forward Euler method on coarser levels, results in a convergence rate up to ten times faster than standard CGKS. In contrast, the implicit lower-upper symmetric Gauss-Seidel (LU-SGS) method offers limited convergence acceleration. Our findings indicate that the explicit multigrid CGKS is highly scalable and effective for large-scale computations, marking a substantial step forward in computational fluid dynamics. |
| title | A Compact Gas-Kinetic Scheme with Scalable Geometric Multigrid Acceleration for Steady-State Computation on 3D Unstructured Meshes |
| topic | Computational Physics |
| url | https://arxiv.org/abs/2402.02075 |