High-order quadrilateral meshes offer superior accuracy and computational efficiency in numerical simulations. However, existing methods struggle to simultaneously preserve boundary/interface features, ensure high quality, and achieve efficient generation, particularly for complex geometries where degenerate and inverted elements frequently occur. To address this issue, this paper proposes a high-quality high-order unstructured quadrilateral mesh generation method based on geometric error-bounded curve reconstruction, which employs an indirect approach to enforce interface consistency. By optimization-based curve reconstruction strategies, our method improves mesh quality while maintaining the validity of high-order elements. Compared to direct high-order mesh optimization techniques, our approach reduces the optimization problem to curve reconstruction problem, significantly lowering computational complexity and enhancing efficiency. Experimental results demonstrate that the proposed method efficiently generates high-quality high-order quadrilateral meshes while preserving boundary/interface geometric features, offering improved adaptability and numerical stability in complex geometries.

翻译：高阶四边形网格在数值模拟中具有优越的精度和计算效率。然而，现有方法难以同时保持边界/界面特征、确保高质量并实现高效生成，尤其在复杂几何中退化单元和反转单元频繁出现。针对这一问题，本文提出一种基于几何误差有界曲线重构的高质量高阶非结构化四边形网格生成方法，采用间接途径强制执行界面一致性。通过基于优化的曲线重构策略，该方法在保持高阶单元有效性的同时提升网格质量。与直接的高阶网格优化技术相比，本文方法将优化问题简化为曲线重构问题，显著降低了计算复杂度并提升了效率。实验结果表明，该方法在保持边界/界面几何特征的前提下，能够高效生成高质量的高阶四边形网格，在复杂几何中展现出更优的适应性和数值稳定性。