Page 47 - 《真空与低温》2025年第4期

真空与低温 第 31 卷 第 4 期
462 Vacuum and Cryogenics 2025 年 7 月

一 种 新 型 的 超 流 氦 二 流 体 模 型 梯 度 项 离 散 方 法

李子兀 1,2 ，张启勇 ，杨鹏程 ，薛 璞 1,2 ，刘世贸 1,2 ，刘志帆 1*
1
1
（1. 中国科学院合肥物质科学研究院，合肥 230031；2. 中国科学技术大学，合肥 230026）

摘要：在超流氦（He II）的二流体模型数值模拟研究中，数值震荡问题一直是学界关注的重点。在二流体模型
离散过程中，传统的体心梯度离散方式在处理温度梯度时存在固有局限性，容易引发数值震荡。这种数值震荡不
仅影响计算结果的准确性，还可能导致模型不稳定。当温度梯度引发的震荡超出一定范围时，会使得模型的计算
结果偏离真实值，严重时甚至可能导致模型崩溃。为此，提出了温度梯度的面梯度离散方法，通过优化离散方式，
有效克服了由体心梯度离散导致的数值震荡。首先对两种离散方式所涉及的方程以及引发数值震荡的原理进行
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了详细阐述，并构建了面梯度离散求解算法。随后，在 OpenFOAM 平台上，以 He II 热对流现象作为计算对象，
将面梯度离散方法应用于其中。通过对数值模拟结果与解析解的对比分析，验证了面梯度离散方法的准确性。
此外，为了进一步评估面梯度离散方法的性能，还对比了使用面梯度离散方法和体心梯度离散方法的数值模拟结
果。结果表明，体心梯度离散方法在数值模拟过程中会出现明显的数值震荡，而面梯度离散方法能够有效抑制这
种震荡。研究为超流氦二流体模型的数值模拟提供了一种更具可靠性和稳定性的离散方法，有助于推动相关领
域的研究进展。
关键词：超流氦；OpenFOAM ；超流体流动传热
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中图分类号：TB69 文献标志码：A 文章编号：1006−7086（2025）04−0462−09
DOI：10.12446/j.issn.1006-7086.2025.04.006

A Novel Method for Discretizing Gradient Terms in Superfluid Helium Two-fluid Model

1,2 1 1 1,2 1,2 1*
LI Ziwu ，ZHANG Qiyong ，YANG Pengcheng ，XUE Pu ，LIU Shimao ，LIU Zhifan
（1. Hefei Institutes of Physical Science，Chinese Academy of Science，Hefei 230031，China；
2. University of Science and Technology of China，Hefei 230026，China）

Abstract：In the research of numerical simulation of the two-fluid model for superfluid helium （He II)，the issue of nu-
merical oscillations has always been a key concern in the academic community. During the discretization process of the two-
fluid model，the traditional cell-centered gradient discretization method has inherent limitations when dealing with tempera-
ture gradients. This method is prone to causing numerical oscillations，which not only affect the accuracy of calculation re-
sults but also may lead to model instability. When the oscillations caused by the temperature gradient exceed a certain range，
the calculation results of the model will deviate from the true values，and in severe cases，it may even lead to model collapse.
To address this problem，this paper proposes a face-gradient discretization method for the temperature gradient. By optimiz-
ing the discretization approach，it effectively overcomes the numerical oscillations caused by the cell-centered gradient dis-
cretization. Specifically，this paper first elaborates on the equations involved in the two discretization methods and the princi-
ples of causing numerical oscillations， and then constructs a face-gradient discretization algorithm. Subsequently， on the
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OpenFOAM platform，taking the thermal counterflow phenomenon of He II as the computational object，the face-gradient
discretization method is applied. Through the comparative analysis of the numerical simulation results and the analytical solu-
tion，the accuracy of the face-gradient discretization method is verified. In addition，to further evaluate the performance of the
face-gradient discretization method，the author also compares the numerical simulation results of using the face-gradient dis-
cretization method and the cell-centered gradient discretization method. The results show that the cell-centered gradient dis-
cretization method will show obvious numerical oscillations during the numerical simulation process，while the face-gradient

收稿日期：2024−12−20
作者简介：李子兀，博士研究生。E-mail：ziwu.li@ipp.ac.cn
通信作者：刘志帆，博士，副研究员。E-mail：zhifan.liu@ipp.ac.cn