布西内斯克近似下速度-压力全耦合求解的伪瞬态延拓方法

蔡海鹏; 李兆仁; 冀文涛; 陶文铨; 朱江楠; 温泉

doi:10.7652/xjtuxb202608007

您当前的位置：

首页 >

文章列表页 >

布西内斯克近似下速度-压力全耦合求解的伪瞬态延拓方法

—————————————————————— | 更新时间：2026-07-28

- 布西内斯克近似下速度-压力全耦合求解的伪瞬态延拓方法
- A Pseudo-Transient Continuation Method for Fully Coupled Velocity-Pressure Solution under the Boussinesq Buoyancy Approximation
- 西安交通大学学报 2026年60卷第8期页码：80-90
- 作者机构：
  
  西安交通大学能源与动力工程学院，710049，西安
  中国航空发动机研究院，101300，北京
- 作者简介：
  
  作者简介：蔡海鹏（2001-），男，硕士生；
  冀文涛（通信作者），男，教授，博士生导师。
- 基金信息：
  
  三维强化结构表面有机工质相变换热微观机理研究(52476089)
- DOI：10.7652/xjtuxb202608007
  中图分类号： TK124
- 收稿：2025-12-23，
  
  网络首发：2026-04-14，
  
  纸质出版：2026-08-10
- 稿件说明：
移动端阅览
蔡海鹏, 李兆仁, 冀文涛, 等. 布西内斯克近似下速度-压力全耦合求解的伪瞬态延拓方法[J]. 西安交通大学学报, 2026,60(8):80-90.

CAI Haipeng, LI Zhaoren, JI Wentao, et al. A Pseudo-Transient Continuation Method for Fully Coupled Velocity-Pressure Solution under the Boussinesq Buoyancy Approximation[J]. Journal of Xi'an Jiaotong University, 2026, 60(8): 80-90.
蔡海鹏, 李兆仁, 冀文涛, 等. 布西内斯克近似下速度-压力全耦合求解的伪瞬态延拓方法[J]. 西安交通大学学报, 2026,60(8):80-90. DOI： 10.7652/xjtuxb202608007.

CAI Haipeng, LI Zhaoren, JI Wentao, et al. A Pseudo-Transient Continuation Method for Fully Coupled Velocity-Pressure Solution under the Boussinesq Buoyancy Approximation[J]. Journal of Xi'an Jiaotong University, 2026, 60(8): 80-90. DOI： 10.7652/xjtuxb202608007.

摘要

针对自然对流布西内斯克浮力近似问题，提出了一种用于压力基速度-压力全耦合求解器的鲁棒性增强与收敛加速方法。首先，将伪瞬态延拓的算法用于求解稳态计算的流体动力学问题，通过构造基于流场物理特征的计算方法来确定伪时间步长，从而替代了传统依赖经验的亚松弛因子；通过阐明该伪时间步长与亚松弛因子在数学上的等效关系，为实现收敛提供一种机制更优路径。其次，在对控制方程进行离散的同时，引入了基于特征速度的尺度分析，通过量化纳维-斯托克斯方程中扩散、对流及浮力项，给出了针对自然对流问题的伪时间步长计算方案。最后，选取环形空腔与梯形空腔两类典型自然对流问题作为验证算例，将提出的算法与一组常见的亚松弛因子（0.20、0.40、0.60、0.80、0.90、0.95）的设置进行了系统对比。研究结果表明：相比于传统亚松弛因子方法，该算法具备较强的自适应性，无需人工调参，其收敛效率即可达到或优于通过大量试算确定的经验性最优松弛因子。同时，在收敛速率与残差控制方面表现的更一致、更稳定。该研究为稳态计算流体动力学求解提供了一种兼具自适应性与最优收敛特性的可靠路径，显著降低了传统方法中对经验调参的依赖。

Abstract

For the Boussinesq buoyancy approximation in natural convection problems

a robustnessenhanced and convergence-accelerated method was proposed for a pressure-based fully coupled velocity-pressure solver. The pseudo-transient continuation method was employed to solve steady-state computational fluid dynamics (CFD) problems. A physics-based calculation method

derived from the flow field characteristics

was developed to determine the pseudo time step

thus replacing the traditional empirically-dependent under-relaxation factors were replaced. The mathematical equivalence between this pseudo time step and the under-relaxation factors was clarified

which provides a more mechanism-optimized way to achieve convergence. During the discretization of the governing equations

a scale analysis based on characteristic velocity was introduced. By quantifying the physical effects of the diffusion

convection

and buoyancy terms in the Navier-Stokes equations

a specific calculation scheme for the pseudo time step tailored to natural convection problems was presented. Finally

two classic natural convection problems—the annular cavity and the trapezoidal cavity—were selected as validation cases. A systematic comparison was conducted between the proposed algorithm and a set of common under-relaxation factors (0.20

0.40

0.60

0.80

0.90

0.95) .The results demonstrate that

compared to the traditional under-relaxation factor approach

the proposed method exhibits remarkable adaptivity. Without any manual parameter tuning

the convergence efficiency of the proposed method is found to match or surpass that of the empirically determined optimal relaxation factors obtained through extensive trial calculations. Furthermore

it exhibits more consistent and stable performance in terms of convergence rate and residual control. This research provides a reliable path for steady-state CFD solvers

offering both self-adaptivity and optimal convergence characteristics

thereby significantly reducing the reliance on empirical parameter tuning inherent in traditional methods.

关键词

Keywords

references

You Wei, Li Zengyao, Tao Wenquan. A general selfadaptive under-relaxation strategy for fast and robust convergence of iterative calculation of incompressible flow [J].Numerical Heat Transfer: Part B Fundamentals,2020,77（4）:299-310.

Gee M W, Kelley C T, Lehoucq R B.Pseudo-transient continuation for nonlinear transient elasticity [J]. International Journal for Numerical Methods in Engineering,2009,78（10）:1209-1219.

刘家宁，杨靖丞，钟文荣，等.超临界氢用空温式气化器的传热特性研究[J].真空与低温，2024，30（4）：408-416.

Liu Jianing, Yang Jingcheng, Zhong Wenrong, et al. Research on heat transfer characteristics of air ambient vaporizer for supercritical hydrogen[J]. Vacuum and Cryogenics, 2024, 30 (4): 408-416.

Ryoo J, Kaminski D, Dragojlovic Z.A residua-l based fuzzy logic algorithm for control of convergence in a computational fluid dynamic simulation[J].Journal of Heat Transfer,1999,121（4）:1076-1078.

Liu Xunliang, Tao Wenquan, Zheng Ping, et al. Control of convergence in a computational fluid dynamic simulation using fuzzy logic [J].Science in China Series: E Technological Science,2002,45（5）:495-502.

Ryoo J, Dragojlovic Z, Kaminski D A.Control of con vergence in a computational fluid dynamics simulation usingANFIS [J].IEEE Transactions on Fuzzy Systems,2005,13（1）:42-47.

商贺，彭敏俊，夏庚磊，等.二维下腔室稳态流场降阶模型开发[J].原子能科学技术，2025，59（10）：2319-2331.

Shang He, Peng Minjun, Xia Genglei, et al. Development of reduced order model for steady state flow field in two-dimensional lower plenum[J]. Atomic Energy Science and Technology, 2025, 59 (10): 2319-2331.

Kelley C T.Numerical methods for nonlinear equations [J].Acta Numerica,2018,27:207-287.

陈曦，于玉贞，程勇刚.非饱和渗流Richards方程数值求解的欠松弛方法[J].岩土力学，2012，33（增刊1）：237-243.

Chen Xi, Yu Yuzhen, Cheng Yonggang. Under-relaxation methods for numerical solution of Richards equation of variably saturated flow[J]. Rock and Soil Mechanics, 2012, 33 (S1): 237-243.

康杰，樊桦，吴东垠.流场特性驱动的亚松弛因子自动获取方法[J].西安交通大学学报，2025，59（4）：40-49.

Kang Jie, Fan Hua, Wu Dongyin. Flow field characteristics-driven automatic under-relaxation factor acquisition method[J]. Journal of Xi'an Jiaotong University, 2025, 59 (4): 40-49.

Stoltze F, Champhekar O, Iranzo A.Upscaling solid oxide electrolysis cell CFD simulations for hydrogen production [J].Engineering Applications of Computational Fluid Mechanics,2025,19（1）:2521529.

Alsaghir A M, Mishra S, Abdallah S, et al. A pseudo-transient pressure gradient method for solving the incompressible Navier-Stokes equations [J].Physics of Fluids,2025,37（1）:013618.

Darwish M, Sraj I, Moukalled F.A coupled finite volume solver for the solution of incompressible flows on unstructured grids [J]. Journal of Computational Physics,2009,228（1）:180-201.

Deng G B, Piquet J, Vasseur X, et al. A new fully coupled method for computing turbulent flows [J]. Computers&Fluids,2001,30（4）:445-472.

刘凯，陈叔平，赵国锋，等.基于流固耦合传热的液氢管道流动特性仿真研究[J].真空与低温，2024， 30（5）：580-588.

Liu Kai, Chen Shuping, Zhao Guofeng, et al. Simulation study on flowing characteristics of liquid hydrogen pipeline based on fluid-solid coupling heat transfer[J]. Vacuum and Cryogenics, 2024, 30 (5): 580-588.

Crawford L, Lemlich R.Natural convection in horizontal concentric cylindrical annuli [J].Industrial &Engineering Chemistry Fundamentals,1962, 1（4）：260-264.

马崇扬，张东辉，邓云，等.具有导热的竖环形封闭腔内自然对流数值研究[J].原子能科学技术，2016， 50（7）：1186-1192.

Ma Chongyang, Zhang Donghui, Deng Yun, et al. Numerical simulation of natural convection in vertical annular enclosed cavity with thermal conduction[J]. Atomic Energy Science and Technology, 2016, 50 (7)：1186-1192.

刘镇涛，肖莉，和琨，等.二维局部受热腔体内电热对流问题模拟和分析[J].力学学报，2021，53（9）：2477-2492.

Liu Zhentao, Xiao Li, He Kun, et al. Numerical study on two-dimensional electro-thermal convection in a partially heated cavity[J]. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53 (9): 2477-2492.

Rhie C M, Chow W L.Numerical study of the turbulent flow past an airfoil with trailing edge separation [J].AIAA Journal,1983,21（11）:1525-1532.

Chen Z J, Przekwas A J.A coupled pressure-based computational method for incompressible/compressible flows [J].Journal of Computational Physics,2010, 229（24）:9150-9165.

Uroi ′ c T, Jasak H, Rusche H.Implicitly coupled pressure-velocity solver [M ] //Nóbrega J M, Jasak H. OpenFOAM ® ：Selected Papers of the 11th Workshop. Cham, Switzerland: Springer International Publishing, 2019:249-267.

Xiao Chengnian, Denner F, van Wachem B G M.Fully-coupled pressure-based finite-volume framework for the simulation of fluid flows at all speeds in complex geometries [J].Journal of Computational Physics, 2017,346:91-130.

Coffey T S, Kelley C T, Keyes D E.Pseudotransient continuation and differential-algebraic equations [J]. SIAM Journal on Scientific Computing,2003,25（2）:553-569.

Kuehn T H, Goldstein RJ.An experimental and theoretical study of natural convection in the annulus between horizontal concentric cylinders [J].Journal of Fluid Mechanics,1976,74（4）:695-719.

Moukalled F, Darwish M.Natural convection in a partitioned trapezoidal cavity heated from the side [J]. Numerical Heat Transfer: Part A Applications, 2003,43（5）:543-563.

浏览量

下载量

CSCD

文章被引用时，请邮件提醒。

提交

工具集

关联资源

流场特性驱动的亚松弛因子自动获取方法

回转误差双目视觉同步测量方法

锂离子电池枝晶内短路的电热特性研究

大型新能源基地综合能源系统协同设计

采用拓扑优化液冷与相变材料协同的大圆柱电池热管理