An Application of Multigrid in Viscous Flow Simulations with Least Squares Isogeometric Method

doi:10.7652/xjtuxb201411021

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An Application of Multigrid in Viscous Flow Simulations with Least Squares Isogeometric Method

更新时间：2025-07-09

- An Application of Multigrid in Viscous Flow Simulations with Least Squares Isogeometric Method
- Vol. 48, Issue 11, Pages: 122-127(2014)
- 作者机构：
  
  西安交通大学机械结构强度与振动国家重点实验室,西安,710049
- 作者简介：
- 基金信息：
- DOI：10.7652/xjtuxb201411021
  CLC： O357.1;O241.82
- Online First：10 November 2014，
  
  Published：2014
- 稿件说明：
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An Application of Multigrid in Viscous Flow Simulations with Least Squares Isogeometric Method[J]. 2014, 48(11): 122-127.
DOI：

An Application of Multigrid in Viscous Flow Simulations with Least Squares Isogeometric Method[J]. 2014, 48(11): 122-127. DOI： 10.7652/xjtuxb201411021.

摘要

针对最小二乘等几何方法模拟黏性流动时条件数大、迭代法收敛速度慢的问题

提出了基于多重网格技术的加速方法。计算中自动生成一系列疏密不同的网格

在最密网格上用最小二乘等几何方法将Navier-Stokes方程离散为代数方程组

用多重网格方法作为独立求解器或共轭梯度法的预处理器迭代求解所得到的代数方程组。对雷诺数为100、400、1 000和2 500的顶盖驱动流进行了数值模拟

计算中进行23次迭代可使方程组的余量降低10个数量级

流动特征量的计算误差在1%以内。计算结果表明

通过多重网格技术加速迭代

提高了最小二乘等几何方法模拟黏性流动的计算效率。

Abstract

A multigrid technique to accelerate iteration is proposed to solve the problem of low convergence rate due to large condition number in simulating viscous flow with the least squares isogeometric method. A series of grids with different element sizes are automatically generated in analysis. The least squares isogeometric method is used to discretize the Navier-Stokes equations into a system of linear equations on the densest grid

and the system is iteratively solved using either the multigrid method as standard solver or the preconditioner of the conjugate gradient method. Numerical simulations are performed on lid driven cavity flow with Re=100

400

1 000 and 2 500. The residual of algebraic equations is reduced about 10 order of magnitude after 23 iterations

and the calculation error on characteristic parameters of the cavity flow is less than 1%. The results show that the performance of the least squares isogeometric method for viscous flow is improved when the multigrid acceleration technique is used.

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references

陈德祥, 徐自力, 刘石, 等. 求解Stokes方程的最小二乘等几何分析方法[J]. 西安交通大学学报, 2013, 47(5): 51-55.

CHEN Dexiang, XU Zili, LIU Shi, et al. Least squares isogeometric analysis for Stokes equation[J]. Journal of Xi'an Jiaotong University, 2013, 47(5): 51-55.

CHEN Dexiang, XU Zili, LIU Shi, et al. Least squares finite element method with high continuity NURBS basis for incompressible Navier-Stokes equations[J]. Journal of Computational Physics, 2014, 260: 204-221.

SAAD Y. Iterative methods for sparse linear systems[M]. Philadelphia, USA: SIAM, 2003.

GAHALAUT K P S, KRAUS J K, TOMAR S K. Multigrid methods for isogeometric discretization[J]. Computer Methods in Applied Mechanics and Engi- neering, 2013, 253: 413-425.

刘石, 陈德祥, 冯永新, 等. 等几何分析的多重网格共轭梯度法[J]. 应用数学和力学, 2014, 25(6): 630-639.

LIU Shi, CHEN Dexiang, FENG Yongxin, et al. A multigrid preconditioned conjugate gradient method for isogeometric analysis[J]. Applied Mathematics and Mechanics, 2014, 25(6): 630-639.

陈德祥, 窦柏通, 徐自力. 最小二乘等几何分析的多重网格方法[J]. 西安交通大学学报, 2014, 48(7): 124-130.

CHEN Dexiang, DOU Baitong, XU Zili. Multigrid least squares isogeometric analysis[J]. Journal of Xi'an Jiaotong University, 2014, 48(7): 124-130.

BRANDT A, LIVNE O E. Multigrid techniques: 1984 guide with applications to fluid dynamics[M]. Philadelphia, USA: SIAM, 2011.

TATEBE O. The multigrid preconditioned conjugate gradient method[C]∥The Sixth Copper Mountain Conference on Multigrid Methods. Copper Mountain, USA: NASA, 1993: 621-634.

TROTTENBERG U, OOSTERLEE C W, SCHULLER A. Multigrid[M]. London, UK: Academic Press, 2000: 28-50.

MARCHI C H, SUERO R, ARAKI L K. The lid-driven square cavity flow: numerical solution with a 1 024×1 024 grid[J]. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 2009, 31(3): 186-198.

ERTURK E, CORKE T C, GOKCOL C. Numerical solutions of 2D steady incompressible driven cavity flow at high Reynolds numbers[J]. International Journal for Numerical Methods in Fluids, 2005, 48(7): 747-774.

BOTELLA O, PEYRET R. Benchmark spectral results on the lid-driven cavity flow[J]. Computers Fluids, 1998, 27(4): 421-433.

RANJAN R, REDDY J N. On multigrid methods for the solution of least-squares finite element models for viscous flows[J]. International Journal of Computational Fluid Dynamics, 2012, 26(1): 45-65.

BRUNEAU C H, SAAD M. The 2D lid-driven cavity problem revisited[J]. Computers Fluids, 2006, 35(3): 326-348.

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