Treatment of Wall Boundary Conditions in High-Order Compact Gas-Kinetic Schemes
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| Format: | Preprint |
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2025
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| _version_ | 1866909527917461504 |
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| author | Zhang, Jiawang Ji, Xing Xu, Kun |
| author_facet | Zhang, Jiawang Ji, Xing Xu, Kun |
| contents | The boundary layer represents a fundamental structure in fluid dynamics, where accurate boundary discretization significantly enhances computational efficiency. This paper presents a third-order boundary discretization for compact gas-kinetic scheme (GKS). Wide stencils and curved boundaries pose challenges in the boundary treatment for high-order schemes, particularly for temporal accuracy. By utilizing a time-dependent gas distribution function, the GKS simultaneously evaluates fluxes and updates flow variables at cell interfaces, enabling the concurrent update of cell-averaged flow variables and their gradients within the third-order compact scheme. The proposed one-sided discretization achieves third-order spatial accuracy on boundary cells by utilizing updated flow variables and gradients in the discretization for non-slip wall boundary conditions. High-order temporal accuracy on boundary cells is achieved through the GKS time-dependent flux implementation with multi-stage multi-derivative methodology. Additionally, we develop exact no-penetration conditions for both adiabatic and isothermal wall boundaries, with extensions to curved mesh geometries to fully exploit the advantages of high-order schemes. Comparative analysis between the proposed one-sided third-order boundary scheme, third-order boundary scheme with ghost cells, and second-order boundary scheme demonstrates significant performance differences for the third-order compact GKS. Results indicate that lower-order boundary cell treatments yield substantially inferior results, while the proposed third-order treatment demonstrates superior performance, particularly on coarse grid configurations. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2503_04493 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Treatment of Wall Boundary Conditions in High-Order Compact Gas-Kinetic Schemes Zhang, Jiawang Ji, Xing Xu, Kun Numerical Analysis Computational Physics The boundary layer represents a fundamental structure in fluid dynamics, where accurate boundary discretization significantly enhances computational efficiency. This paper presents a third-order boundary discretization for compact gas-kinetic scheme (GKS). Wide stencils and curved boundaries pose challenges in the boundary treatment for high-order schemes, particularly for temporal accuracy. By utilizing a time-dependent gas distribution function, the GKS simultaneously evaluates fluxes and updates flow variables at cell interfaces, enabling the concurrent update of cell-averaged flow variables and their gradients within the third-order compact scheme. The proposed one-sided discretization achieves third-order spatial accuracy on boundary cells by utilizing updated flow variables and gradients in the discretization for non-slip wall boundary conditions. High-order temporal accuracy on boundary cells is achieved through the GKS time-dependent flux implementation with multi-stage multi-derivative methodology. Additionally, we develop exact no-penetration conditions for both adiabatic and isothermal wall boundaries, with extensions to curved mesh geometries to fully exploit the advantages of high-order schemes. Comparative analysis between the proposed one-sided third-order boundary scheme, third-order boundary scheme with ghost cells, and second-order boundary scheme demonstrates significant performance differences for the third-order compact GKS. Results indicate that lower-order boundary cell treatments yield substantially inferior results, while the proposed third-order treatment demonstrates superior performance, particularly on coarse grid configurations. |
| title | Treatment of Wall Boundary Conditions in High-Order Compact Gas-Kinetic Schemes |
| topic | Numerical Analysis Computational Physics |
| url | https://arxiv.org/abs/2503.04493 |