An effective implementation of high-order compact gas-kinetic scheme on structured meshes for compressible flows
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908486644793344 |
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| author | Yang, Yaqing Zhao, Fengxiang Xu, Kun |
| author_facet | Yang, Yaqing Zhao, Fengxiang Xu, Kun |
| contents | A novel fifth-order compact gas-kinetic scheme is developed for high-resolution simulation of compressible flows on structured meshes. Its accuracy relies on a new multidimensional fifth-order compact reconstruction that uses line-averaged derivatives to introduce additional degrees of freedom, enabling a compact stencil with superior resolution. For non-orthogonal meshes, reconstruction is performed on a standard reference cell in a transformed computational space. This approach provides a unified polynomial form, significantly reducing memory usage and computational cost while simplifying implementation compared to direct multi-dimensional or dimension-by-dimension methods. A nonlinear adaptive method ensures high accuracy and robustness by smoothly transitioning from the high-order linear scheme in smooth regions to a second-order scheme at discontinuities. The method is implemented with multi-GPU parallelization using CUDA and MPI for large-scale applications. Comprehensive numerical tests, from subsonic to supersonic turbulence, validate the scheme's high accuracy, resolution and excellent robustness. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_08965 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An effective implementation of high-order compact gas-kinetic scheme on structured meshes for compressible flows Yang, Yaqing Zhao, Fengxiang Xu, Kun Numerical Analysis A novel fifth-order compact gas-kinetic scheme is developed for high-resolution simulation of compressible flows on structured meshes. Its accuracy relies on a new multidimensional fifth-order compact reconstruction that uses line-averaged derivatives to introduce additional degrees of freedom, enabling a compact stencil with superior resolution. For non-orthogonal meshes, reconstruction is performed on a standard reference cell in a transformed computational space. This approach provides a unified polynomial form, significantly reducing memory usage and computational cost while simplifying implementation compared to direct multi-dimensional or dimension-by-dimension methods. A nonlinear adaptive method ensures high accuracy and robustness by smoothly transitioning from the high-order linear scheme in smooth regions to a second-order scheme at discontinuities. The method is implemented with multi-GPU parallelization using CUDA and MPI for large-scale applications. Comprehensive numerical tests, from subsonic to supersonic turbulence, validate the scheme's high accuracy, resolution and excellent robustness. |
| title | An effective implementation of high-order compact gas-kinetic scheme on structured meshes for compressible flows |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2508.08965 |