Abstract A hyperbolic method for incompressible Navier-Stokes equations is presented in a cell-centered finite volume framework on unstructured meshes. Solution algorithms were introduced on triangular meshes in 2D and on tetrahedral meshes in 3D. Justification of the absolute Jacobian approximation is discussed, and a solution reconstruction algorithm utilizing the robust and effective wrapping stencil is illustrated. The effectiveness of the unconditionally stable implicit solution strategy was demonstrated by comparison to an explicit scheme. A series of test cases are presented in order of study accuracy and as a comparison with other reference computational and experimental results, namely Kovasznay flow, driven cavity flow, and flow past a circular cylinder in 2D and a sphere in 3D. The equal order of accuracy feature of the hyperbolic method, namely the second order accuracy in solution and the gradient variables, was verified. The superior accuracy of the current hyperbolic scheme in terms of predicting the velocity gradient on a solid surface was emphasized by comparison with standard second order finite volume results.

中文翻译：

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非结构网格上稳态不可压缩纳维-斯托克斯方程的双曲细胞中心有限体积法

摘要 在非结构化网格上以单元为中心的有限体积框架中，提出了不可压缩Navier-Stokes方程的双曲线方法。在 2D 中的三角形网格和 3D 中的四面体网格上引入了求解算法。讨论了绝对雅可比近似的证明，并说明了利用稳健有效的包装模板的解决方案重建算法。通过与显式方案的比较，证明了无条件稳定隐式求解策略的有效性。一系列测试案例按照研究准确性的顺序呈现，并与其他参考计算和实验结果进行比较，即 Kovasznay 流、驱动腔流以及 2D 中的圆柱流和 3D 中的球体流。验证了双曲线方法的等阶精度特征，即解中的二阶精度和梯度变量。通过与标准二阶有限体积结果的比较，强调了当前双曲线方案在预测固体表面上的速度梯度方面的优越精度。