Abstract: In this paper, two-level stabilized finite volume methods are considered which are based on local Gauss integral technique and two-level grid algorithm for the incompressible flow. The error analysis shows that the two-level stabilized finite volume methods provide an approximate solution with the convergence rate of the same order as the usual stabilized finite volume solution solving the incompressible flow problems on a fine grid for a related choice of mesh widths. The performance of three kinds iterative scheme of two-level stabilized methods are compared in efficiency and precision aspects by a series of numerical experiments. It discovers that the simple scheme is better than two others on accuracy and efficiency. There is the poor numerical accuracy for the Newton scheme, but the Picard scheme is more suitable to incompressible flow with low viscosity coefficient.

Key words: incompressible flow, finite volume methods, two-level stabilized methods, Navier-Stokes equations

摘要： 通过将局部高斯积分稳定化方法和两重网格算法思想紧密结合，提出了粘性不可压缩流体的两重稳定有限体积算法。将该算法的三种迭代格式进行了效率的分析比较。理论分析和数值实验发现：当粗、细网格尺度比例选择适当时，两重算法与传统算法具有相同精度解的同时，效率大大提高；对不同格式的两重有限体积算法进行比较分析发现：Simple格式计算效率最高，Picard格式次之，Newton格式较低。

关键词: 不可压缩流体, 有限体积算法, 两重稳定方法, Navier-Stokes方程