DGSEM框架内基于熵黏性的两相流耦合求解方法

张天翼; 郝世熙; 赵明; 刘正先

doi:10.13224/j.cnki.jasp.20250022

DGSEM框架内基于熵黏性的两相流耦合求解方法

doi: 10.13224/j.cnki.jasp.20250022

天津大学机械工程学院，天津 300350

基金项目: 国家重点研发计划（2022YFB2402800）；国家自然科学基金面上项目（12372289）；天津市重点基金（22JCZDJC00910）

详细信息

作者简介:
张天翼（1999-），男，硕士生，主要从事计算流体力学研究

通讯作者:
赵明（1985-），男，副教授、博士生导师，博士，主要从事计算流体力学研究。E-mail：ming.zhao@tju.edu.cn

中图分类号: V228.3
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- 文章访问数: 230
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- 被引次数: 0
出版历程
- 收稿日期: 2025-01-14
- 网络出版日期: 2026-05-11

Coupled two-phase flow solver based on entropy viscosity within DGSEM framework

School of Mechanical Engineering，Tianjin University，Tianjin 300350，China

摘要

摘要:
在可压缩两相流数值模拟中为解决激波、物质界面等间断问题导致的精度下降和Gibbs等现象，实现间断的精确解析，提出一种基于间断谱元法（discontinuous Galerkin spectral element method，DGSEM）框架的耦合方法。该方法通过熵黏性模型自动区分激波与接触间断，自适应地添加人工黏性解决单相间断问题；并基于DGSEM方法离散水平集（level-set）方程，结合虚拟流体方法实现了两相界面的准确追踪以及与流场的耦合求解。结果表明该方法在光滑区域可以达到设计精度，相比变量阶跃型人工黏性和5阶weighted essentially non-oscillatory-Z（WENO-Z）格式，减少了过耗散得到了更多流场细节；在仅使用1/4网格密度的情况下，得到的监测点数据与实验结果的误差比同样采用间断有限元但使用耗散类型界面模型的计算结果最多降低了6.4%，证明该方法有效提升了间断捕捉和与物质界面追踪的精度。
- 多相流 /
- 激波捕捉 /
- DGSEM /
- 熵黏性 /
- level-set方法 /
- 虚拟流体方法
Abstract:
To deal with the issues of accuracy degradation and Gibbs phenomena caused by discontinuities such as shock waves, contact discontinuities, and free interfaces in the numerical simulation of compressible two-phase flows, a coupled solution method was developed based on the discontinuous Galerkin spectral element method (DGSEM) framework. To address the issue of discontinuities in single phase, an entropy viscosity model that can automatically distinguish shocks from contact discontinuities and adaptively add artificial viscosity was introduced. The solution method was also coupled with the level-set method, which was discretized by the DGSEM framework and combined with the ghost fluid approach to accurately track the material interface and solve the flow field simultaneously. Numerical results showed that this method can achieve the designed accuracy in smooth regions. Compared with the variable-step artificial viscosity and the fifth-order weighted essentially non-oscillatory-Z (WENO-Z) scheme, it reduced over-dissipation and obtained more flow-field details. Compared with calculations using the same discontinuous Galerkin method but with dissipative interface models, this method reduced the error at monitoring points by up to 6.4% compared with experimental results when using only one-fourth of the grid density. This proved that the method can effectively improve the accuracy of discontinuity capture and material interface tracking.
- multiphase flow /
- shock capturing /
- DGSEM /
- entropy viscosity /
- level-set method /
- ghost fluid method

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图 1 一维Sod问题（t=0.5）

Figure 1. One-dimensional Sod’s problem （t=0.5）

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图 2 二维Riemann问题1（t=0.3）

Figure 2. Two-dimensional Riemann problem 1 （t=0.3）

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图 3 二维Riemann问题2计算结果（t=0.2）

Figure 3. Result of two-dimensional Riemann problem 2 （t=0.2）

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图 4 二维Riemann问题3计算结果（t=0.8）

Figure 4. Result of two-dimensional Riemann problem 3（t=0.8）

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图 5 移动界面问题（t=0.0165）

Figure 5. Translate interface （t=0.0165）

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图 6 虚拟流体方法

Figure 6. Ghost fluid method

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图 7 虚拟流体方法求解移动界面问题（t=0.4）

Figure 7. Translate interface solved by ghost fluid method （t=0.4）

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图 8 激波-物质界面相互作用问题（t=0.3）

Figure 8. Shock-free interface interaction problem （t=0.3）

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图 9 虚拟流体方法求解两相Sod问题（t=0.4）

Figure 9. Sod’s problem with double phase solved by ghost fluid method （t=0.4）

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图 10 有无熵黏性的两相Sod问题（t=0.4）

Figure 10. Sod’s problem with double phase with and without entropy viscosity （t=0.4）

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图 11 激波-R22气泡相互作用

Figure 11. Shock wave-R22 bubble interaction

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图 12 激波-氦气气泡相互作用

Figure 12. Shock wave-helium bubble interaction

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图 13 激波-氦气气泡相互作用

Figure 13. Shock wave-helium bubble interaction

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表 1 正弦波测试算例（有人工黏性）

Table 1. Sine wave test case （with artificial viscosity）

网格量	k=3		k=4
网格量	$ {L}_{2} $误差	收敛率	$ {L}_{2} $误差	收敛率
20	9.98199×10⁻⁴		2.24598×10⁻⁵
40	1.26448×10⁻⁴	2.98	1.24348×10⁻⁶	4.18
80	1.57069×10⁻⁵	3.00	7.59415×10⁻⁸	4.03
160	1.95116×10⁻⁶	3.02	4.7153×10⁻⁹	4.00

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表 2 正弦波测试算例（无人工黏性）

Table 2. Sine wave test case（without artificial viscosity）

网格量	k=3		k=4
网格量	$ {L}_{2} $误差	收敛率	$ {L}_{2} $误差	收敛率
20	9.24106×10⁻⁴		2.01887×10⁻⁵
40	1.22672×10⁻⁴	2.91	1.20678×10⁻⁶	4.06
80	1.55342×10⁻⁵	2.98	7.54001×10⁻⁸	4.00
160	1.94273×10⁻⁶	3.00	4.70908×10⁻⁹	4.00

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表 3 二维激波-气泡算例初值设置

Table 3. Initial condition setup of two-dimensional shock-bubble interaction

气体	$ \gamma $	$ \rho $	$ u $	$ v $	$ p $
波前空气	1.4	1.40000	0	0	1.00000
波后空气	1.4	1.92691	0.33361	0	1.56980
氦气	1.648	0.25463	0	0	1.00000
R22	1.249	4.41540	0	0	1.00000

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表 4 激波-R22气泡问题波速对比

Table 4. Wave speed comparison of shock wave-R22 bubble problem

方法	$ {c}_{\mathrm{s}} $/（m/s）	$ {c}_{\mathrm{r}} $/（m/s）	$ {c}_{\mathrm{i}} $/（m/s）
本文	419	239	73
Naber^[25]	419	230	73
Quirk和Karni^[27]	420	254	70
Wackers和Koren^[28]	419	241	75
实验数据^[26]	415	240	73

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表 5 激波-氦气气泡问题波速对比

Table 5. Wave speed comparison of shock wave-helium bubble problem

方法	$ {c}_{\mathrm{s}} $/（m/s）	$ {c}_{\mathrm{r}} $/（m/s）	$ {c}_{\mathrm{i}} $/（m/s）
本文	419	897	180
Naber^[25]	419	955	181
Quirk和Karni^[27]	422	943	178
Wackers和Koren^[28]	419	950	173
实验数据^[26]	410	900	170

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