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姜昌伟, 谢云峰, 石尔, 刘代飞, 李杰, 胡章茂. 基于侵入混沌多项式法的随机多孔介质内顺磁性流体热磁对流不确定度量化. 力学学报, 2022, 54(1): 106-118. DOI: 10.6052/0459-1879-21-427
引用本文: 姜昌伟, 谢云峰, 石尔, 刘代飞, 李杰, 胡章茂. 基于侵入混沌多项式法的随机多孔介质内顺磁性流体热磁对流不确定度量化. 力学学报, 2022, 54(1): 106-118. DOI: 10.6052/0459-1879-21-427
Jiang Changwei, Xie Yunfeng, Shi Er, Liu Daifei, Li Jie, Hu Zhangmao. Uncertainty quantification for thermomagnetic convection of paramagnetic fluid in random porous media based on intrusive polynomial chaos method. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(1): 106-118. DOI: 10.6052/0459-1879-21-427
Citation: Jiang Changwei, Xie Yunfeng, Shi Er, Liu Daifei, Li Jie, Hu Zhangmao. Uncertainty quantification for thermomagnetic convection of paramagnetic fluid in random porous media based on intrusive polynomial chaos method. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(1): 106-118. DOI: 10.6052/0459-1879-21-427

基于侵入混沌多项式法的随机多孔介质内顺磁性流体热磁对流不确定度量化

UNCERTAINTY QUANTIFICATION FOR THERMOMAGNETIC CONVECTION OF PARAMAGNETIC FLUID IN RANDOM POROUS MEDIA BASED ON INTRUSIVE POLYNOMIAL CHAOS METHOD

  • 摘要: 目前流体流动与传热问题的研究大都基于确定性工况条件, 而现实流体流动与传热问题中存在着大量不确定性因素, 计算流体力学的不确定性量化提供了一种理解流体物性、边界条件与初始条件等不确定性因素对模拟结果影响的能力. 为揭示随机多孔介质内顺磁性流体热磁对流的传播规律与演化特征, 本文发展了一种基于侵入式多项式混沌展开法的热磁对流不确定性量化数理模型与算法程序. 该方法分别利用Karhunen-Loeve展开与多项式混沌展开表达输入随机参数与输出响应量, 同时利用伽辽金投影方法将随机热磁对流控制方程解耦为一组可以应用有限元修正方法求解的确定性控制方程, 并对输出响应量多项式混沌进行求解, 最后采用随机投影法求解相应的确定性控制方程中的混沌系数, 得到输出响应量的统计特征与混沌效应. 热磁对流不确定性量化表明多孔介质孔隙率不确定性通过控制方程演化, 进而影响着多孔介质方腔内顺磁性流体热磁对流, 顺磁性流体热磁对流呈现出显著的混沌效应. 与蒙特卡罗法预测结果相比, 两者计算结果吻合良好, 但侵入式混沌多项式展开法计算量显著减少.

     

    Abstract: At present, the research of fluid flow and heat transfer problems is mostly based on deterministic working conditions, but there are a large number of uncertain factors in real fluid flow and heat transfer problems. The uncertainty quantification of computational fluid dynamics provides an ability to understand the influence of uncertain factors such as fluid physical properties, boundary conditions and initial conditions on simulations results. In order to reveal the propagation law and evolution characteristics of thermomagnetic convection of paramagnetic fluid in random porous media, a mathematical model and algorithm program of uncertainty quantification for thermomagnetic convection were developed based on intrusive polynomial chaos expansion method. In this method, the input random parameters and output response were expressed by Karhunen-Loeve expansion and polynomial chaos expansion respectively. At the same time, the Galerkin projection method was adopted to decouple the stochastic control equations into a set of deterministic control equations which can be solved by finite element correction method, and each polynomial chaos of output response was solved. Finally, the stochastic projection method was used to solve the chaos coefficients in the corresponding deterministic control equations, and the statistical characteristics and chaos effect of the output response are obtained. The uncertainty quantification of thermomagnetic convection shows that the porosity uncertainty of porous media affects the thermomagnetic convection of paramagnetic fluid in a square cavity through the evolution of governing equations, and the thermomagnetic convection of paramagnetic fluid presents a significant chaos effect. The output response shows the characteristics of rapid convergence. The output response values in the first-order mode are at least one order of magnitude lower than the corresponding average values, while the output response values in the second-order mode are much smaller than those in the first-order mode. Compared with the Monte Carlo method, the two results agree well, but the computational cost of the intrusive polynomial chaos expansion method is significantly reduced.

     

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