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arXiv · 2508.08965

An effective implementation of high-order compact gas-kinetic scheme on structured meshes for compressible flows

Yaqing Yang·Fengxiang Zhao·Kun Xu
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Abstract

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.

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Yaqing Yang, Fengxiang Zhao, Kun Xu. 2025-08-12. An effective implementation of high-order compact gas-kinetic scheme on structured meshes for compressible flows. https://arxiv.org/abs/2508.08965

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