Abstract In this article, a finite volume formulation for solving the Navier-Stokes equations using unstructured hybrid grids and a staggered arrangement of variable pressure and velocity is presented. In this manner, a tight spatial pressure-velocity coupling is ensured without compromising geometrical flexibility. A second contribution of this work lays upon proposing a suitable interpolation function for the convected velocities in the momentum equations. For this purpose, we employ the so-called “Physical Influence Scheme (PIS),” which fully incorporates all physical phenomena involved, namely convection, diffusion, and pressure effects. Each term corresponding to each physical phenomenon is carefully addressed. We present numerical experiments that show the suitability of the PIS for the staggered finite volume formulation and highlight the importance of including diffusion and pressure effects (in addition to convection) into the interpolation function.

中文翻译：

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物理影响方案应用于交错非结构化网格以解决流体流动问题

摘要 在本文中，提出了使用非结构化混合网格和可变压力和速度的交错排列来求解 Navier-Stokes 方程的有限体积公式。以这种方式，在不影响几何灵活性的情况下确保了紧密的空间压力-速度耦合。这项工作的第二个贡献在于为动量方程中的对流速度提出了一个合适的插值函数。为此，我们采用了所谓的“物理影响方案 (PIS)”，它完全包含了所有涉及的物理现象，即对流、扩散和压力效应。对应于每个物理现象的每个术语都经过仔细处理。