A 2D compact fourth-order projection decomposition method
A 2D compact fourth-order projection decomposition method
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DOI：
10.1016/j.jcp.2004.12.005
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发表时间：
2005-06
影响因子：
4.1
通讯作者：
S. Abide;S. Viazzo
中科院分区：
文献类型：
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作者：
S. Abide;S. Viazzo
设计了一种求解多连通矩形域中不可压缩粘性流的二维四阶紧致直接格式投影分解方法。在每个子域中，控制纳维-斯托克斯方程通过在空间上使用四阶紧格式和在时间上使用二阶格式来离散化。子域之间的耦合基于直接非重叠多域方法：它允许解决复杂几何中投影方法产生的每个亥姆霍兹/泊松问题。泊松-诺依曼问题可解性的主要困难得到解决和正确处理。通过一些经典的数值实验对现有的数值方法进行了检验。首先，通过与泰勒问题的解析解相匹配，展示了时间上的二阶精度和空间上的四阶精度。该方法还通过模拟 2D 盖驱动腔中的流动进行了测试。其他两个基准问题进一步说明了紧凑方案投影分解方法的实用性，即向后台阶上的流动和经过方形棱柱的层流。目前的结果与实验数据和文献中提供的其他数值解非常吻合。
A 2D fourth-order compact direct scheme projection decomposition method for solving incompressible viscous flows in multi-connected rectangular domains is devised. In each subdomain, the governing Navier–Stokes equations are discretized by using fourth-order compact schemes in space and second-order scheme in time. The coupling between subdomains is based on a direct non-overlapping multidomain method: it allows to solve each Helmholtz/Poisson problem resulting of a projection method in complex geometries. The major difficulty of the Poisson–Neumann problem solvability is addressed and correctly treated. The present numerical method is checked through some classical numerical experiments. First, the second-order accuracy in time and the fourth-order accuracy in space are shown by matching with the analytical solution of the Taylor problem. The method is also tested by simulating the flow in a 2D lid-driven cavity. The utility of the compact scheme projection decomposition method approach is further illustrated by two other benchmark problems, viz., the flow over a backward-facing step and the laminar flow past a square prism. The present results are in good agreement with the experimental data and other numerical solutions available in the literature.