基于自适应法向射线加密的笛卡尔网格流体仿真方法
CARTESIAN GRID FLUID SIMULATION METHOD BASED ON ADAPTIVE NORMAL RAY REFINEMENT
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摘要: 在黏性流动模拟中, 近壁流动在物面法向方向上的速度梯度远大于切线方向, 呈现出显著的各向异性特征. 传统的各向同性笛卡尔网格方法在捕捉边界层流动细节时面临网格数量剧增和计算效率下降的挑战. 针对这一问题, 提出了一种基于自适应法向射线加密(adaptive normal ray refinement, ANRR)的笛卡尔网格黏性流体仿真方法. 该方法的核心要义在于, 根据物面切线方向上的角度变化程度来自适应生成法向射线种子点, 在法向射线附近进行网格加密, 以精确捕捉边界层流动特征, 同时在射线之间采用较粗糙的网格过渡, 从而在保证计算精度的前提下有效减少整体网格数量. 然后利用插值构建了射线间的高效信息传递技术, 确保流场求解过程中的准确性. 最后, 对层流平板、低雷诺数圆柱绕流以及NACA0012翼型绕流等典型算例进行模型验证. 结果表明, 与传统几何自适应加密网格方法相比, ANRR网格方法在边界层流动区域显著减少了网格规模, 在保持高精度的同时提升了计算效率, 为自适应笛卡尔网格的黏性流动问题高效求解提供了新的解决方案.Abstract: In viscous flow simulations, the velocity gradient in the normal direction of the wall is much larger than that in the tangential direction, presenting a significant anisotropic feature. Traditional isotropic Cartesian grid methods face the challenges of a sharp increase in the number of grids and a decline in computational efficiency when capturing the details of boundary layer flows. To address this issue, this paper proposes a Cartesian grid viscous fluid simulation method based on Adaptive Normal Ray Refinement (ANRR). The core of this method lies in adaptively generating normal ray seed points according to the degree of angle change in the tangential direction of the surface, and performing grid refinement near the normal rays to accurately capture the characteristics of boundary layer flows. Meanwhile, coarser grids are used for transition between rays, effectively reducing the overall number of grids while maintaining computational accuracy. Then, an efficient information transfer technology between rays is constructed through interpolation to ensure the accuracy of the flow field solution process. Finally, typical cases such as laminar flow over a flat plate, low Reynolds number flow around a circular cylinder, and flow around an NACA0012 airfoil are used for model verification. The results show that compared with the traditional geometric adaptive grid refinement method, the ANRR grid method significantly reduces the grid scale in the boundary layer flow region, improves computational efficiency while maintaining high accuracy, and provides a new solution for the efficient solution of viscous flow problems using adaptive Cartesian grids.