This paper presents a numerical method for incompressible fluid flow. A difficulty in analyzing incompressible fluid flow is that the continuity equation has no time evolution term. In the marker and cell (MAC) method, Poisson’s equation is solved iteratively, which takes most of the computation time, and in the artificial compressibility method (ACM), pseudo-time iteration is necessary to solve for unsteady solutions. Here, modal analysis that uses the velocity eigenvectors corresponding to zero eigenvalues is proposed for analyzing two-dimensional incompressible fluid flow. The proposed method involves only about one third of the number of variables needed in the MAC method and the ACM, and it does not require iterative calculation of Poisson’s equation or pseudo-time iteration. Numerical results for a simple flow system and a cavity flow obtained using the proposed method are compared with those obtained using the ACM and the simplified MAC method. The results agree well, thereby validating the proposed modal analysis.

中文翻译：

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不可压缩流体流动的模态分析

本文提出了不可压缩流体流动的数值方法。分析不可压缩流体流动的一个困难是连续性方程没有时间演化项。在标记和单元（MAC）方法中，泊松方程是迭代求解的，这占用了大部分计算时间，而在人工压缩方法（ACM）中，需要伪时间迭代来求解非稳态解。这里，提出了使用与零特征值相对应的速度特征向量的模态分析来分析二维不可压缩流体流动。所提出的方法仅涉及MAC方法和ACM所需变量数量的大约三分之一，并且不需要泊松方程的迭代计算或伪时间迭代。将使用该方法获得的简单流动系统和空腔流动的数值结果与使用 ACM 和简化 MAC 方法获得的数值结果进行了比较。结果非常吻合，从而验证了所提出的模态分析。