An Adaptive Cartesian Grid Method for the Incompressible Navier-Stokes Equations

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An Adaptive Cartesian Grid Method for the Incompressible Navier-Stokes Equations

更新时间：2025-07-09

- An Adaptive Cartesian Grid Method for the Incompressible Navier-Stokes Equations
- Vol. 43, Issue 11, Pages: 11-17(2009)
- 作者机构：
  
  1. 西安交通大学能源与动力工程学院,西安,710049
  2. 西安交通大学人居环境与建筑工程学院,西安,710049
  3. 日本理化学研究所VCAD模拟研究室, 351-0198, 日本和光市
- 作者简介：
- 基金信息：
- DOI：
  CLC： TK124
- Online First：10 November 2009，
  
  Published：2009
- 稿件说明：
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An Adaptive Cartesian Grid Method for the Incompressible Navier-Stokes Equations[J]. 2009, 43(11): 11-17.
DOI：

An Adaptive Cartesian Grid Method for the Incompressible Navier-Stokes Equations[J]. 2009, 43(11): 11-17. DOI：

摘要

提出了一种用直角网格表达背景、切削网格表达边界的非结构化自适应直角网格方法.该方法采用四叉树保存网格数据

将切削简化成6种类型

用速度的旋度和散度作为自适应加密标准

从而可实现任意二维区域网格的自动生成和自适应加密.通过将极小网格边界化处理

利用SIMPLE算法处理速度和压力的耦合

实现了该网格上N-S方程的离散和求解.算例表明

该方法网格生成简单

可以用于任意形状上的流动和传热模拟

相比非自适应方法

用一半的网格数目即可达到相同的计算精度.

Abstract

An adaptive unstructured grid generation algorithm

which adopts Cartesian grid to decompose a background domain and adopts a cut cell approach to express curvilinear boundaries

is presented for solving steady incompressible Navier-Stokes equations. By using quadtree data structure to store mesh data

simplifying cut types into six schemes

and employing the curl and divergence of velocity as criteria of grid refinement

this approach can implement mesh generation and adaptive refinement for arbitrary complex geometries automatically. A solution of N-S equations via finite volume method for this mesh is derived. The SIMPLE based smoothing pressure correction is chosen to suppress the checkerboard pressure oscillation due to collocated variables arrangement. The present method is applied to two benchmark problems and is verified to be accurate and efficient.

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references

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