基于曲线坐标系统的MAC方法简化数值模型
A numerical model based on the curvilinear coordinate system for the MAC method simplified
AI总结：
本文提出了一种基于曲线坐标系统的简化MAC方法，用于研究无自由面的不可压缩流体流动，通过参数化样条构建边界面几何，并采用有限差分和FOU方案进行数值计算，验证了该方法在平行板、顶盖驱动腔和动脉粥样硬化问题中的有效性。
摘要：
在本文中，我们开发了一种数值方法，用于研究无自由面的不可压缩流体流动，该方法基于曲线坐标系统，并通过参数化样条构造边界面几何。首先，我们讨论了纳维-斯托克斯方程和连续性方程在曲线坐标系统中的表示，以及辅助条件。然后，我们介绍了数值方法——简化版的MAC（Marker and Cell）方法，并展示了控制方程的离散化过程，该过程采用有限差分法和FOU（First Order Upwind）方案进行实现。最后，我们将该数值方法应用于平行板问题、顶盖驱动腔问题和动脉粥样硬化问题，并将所得结果与文献中的结果进行了比较。
英文摘要：
In this paper we developed a numerical methodology to study some incompressible fluid flows without free surface, using the curvilinear coordinate system and whose edge geometry is constructed via parametrized spline. First, we discussed the representation of the Navier-Stokes and continuity equations on the curvilinear coordinate system, along with the auxiliary conditions. Then, we presented the numerical method -- a simplified version of MAC (\textit{Marker and Cell}) method -- along with the discretization of the governing equations, which is carried out using the finite differences method and the implementation of the FOU (\textit{First Order Upwind}) scheme. Finally, we applied the numerical methodology to the parallel plates problem, lid-driven cavity problem and atherosclerosis problem, and then we compare the results obtained with those presented in the literature. Keywords: finite differences, simplified MAC, curvilinear coordinates, parallel plates, did-driven cavity, atherosclerosis.
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