基于PPM的界面压缩方法研究

陈芳; 李平; 刘坤; 柏劲松; 林健宇; 季路成

doi:10.11858/gywlxb.20180663

基于PPM的界面压缩方法研究

doi: 10.11858/gywlxb.20180663

陈芳^{1, 2,},
李平^1,*, ,,
刘坤¹,
柏劲松¹,
林健宇¹,
季路成²

1.
中国工程物理研究院流体物理研究所，四川绵阳　621999
2.
北京理工大学宇航学院，北京　100081

基金项目: 国家自然科学基金（11532012，51676015）

详细信息

作者简介:
陈　芳（1990－），女，博士研究生，主要从事可压缩多相流模拟研究.E-mail：cocochen1929@163.com

通讯作者:
李　平（1966－），男，博士，研究员，主要从事爆炸力学及冲击动力学理论与数值计算方法研究. E-mail：lp0703@263.net

中图分类号: O359.1
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出版历程
- 收稿日期: 2018-10-18
- 修回日期: 2018-11-16

Interface Compression Technique in PPM

CHEN Fang^{1, 2
,},
LI Ping^{1,*
, ,},
LIU Kun¹,
BAI Jingsong¹,
LIN Jianyu¹,
JI Lucheng²

1.
Institute of Fluid Physics, CAEP, Mianyang 621999, China
2.
School of Aerospace Engineering, Beijing Institute of Technology, Beijing 100081, China

摘要

摘要: 高精度多组分分段抛物线法（Piecewise Parabolic Method，PPM）在对可压缩多相流问题进行模拟计算时，在不同组分交界面上存在界面扩散。为此，通过引入包含界面压缩和密度修正的人工界面压缩方法，抑制界面扩散现象。采用一个界面函数表示运动的物质界面，在多组分质量守恒方程和输运方程中添加考虑人工压缩和人工黏性的压缩源项，并在伪时间内采用二阶中心差分法和两步Runge-Kutta方法进行离散求解，采用Strang型分裂格式实现了整体算法的时间二阶精度。一维与二维数值模拟试验表明，结合人工界面压缩之后的PPM能有效抑制界面上数值扩散问题，在长时间的数值模拟中，人工界面压缩能够将扩散界面厚度维持在一定网格之内且保持界面形状不改变，尤其对于涉及稀疏波的问题，如激波引起的水中气泡坍塌，界面压缩效果更为显著。
- 分段抛物线法 /
- 可压缩多相流 /
- 界面压缩 /
- 激波捕捉
Abstract: This paper describes an artificial interface compression technique for the multi-fluid piecewise parabolic method (PPM). The proposed approach enables the simulation of interfaces between compressible multi-fluid flows with high density ratios and strong shock waves. A compression source term incorporated both interface compression and density correction is added to the mass conservation equation. The compression source term is solved in pseudo-time steps using the interface compression technique and the advection part is solved by multi-fluid PPM. The Strang splitting algorithm achieves second-order accuracy by combining the solutions of the advection operator and the interface compression operator. Numerical tests on the interaction of shock waves with interfaces in compressible multi-fluid flows reveal that multi-fluid PPM combined with the artificial interface compression technique can effectively prevent the smearing phenomenon, which is often observed at the contact interface. For long-time simulations, artificial interface compression with interface sharpening can constrain the thickness of the diffused interface to a few cells and maintain the interface profile. This artificial interface compression technique works well with multi-fluid PPM and the effect is obvious. It is a significant step in the accurate simulation of the collapse of air cavities in water, which involves strong rarefaction waves.
- piecewise parabolic method /
- compressible multi-fluid flows /
- interface compression /
- shock capturing

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图 1 一维纯对流问题

Figure 1. Solution of the one-dimensional advection test

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图 2 水中气泡坍塌问题示意图(初始状态)

Figure 2. Air cavity collapse in water test (Description of the initial conditions)

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图 3 水中气泡坍塌问题的界面函数分布图

Figure 3. Air cavity collapse in water test （Mapping of the interface function）

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图 4 水中气泡塌陷问题的密度（上）与界面函数（下）分布图(${\Delta x =\Delta y = 0.006\;25}$)

Figure 4. Air cavity collapse in water test (Mapping of the density (top half) and the interface function (bottom half), computed with ${\Delta x =\Delta y = 0.006\;25}$)

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图 5 轴线上的界面函数分布(“●” 和“□”分别表示有、无AIC)

Figure 5. Profile of the interface function along the axis y = 0 with (●) and without (□) AIC

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图 6 空气-R22气柱相互作用示意图(初始状态)

Figure 6. Air-R22 shock-cylinder interaction test（Description of the initial conditions）

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图 7 不同时刻的界面分布

Figure 7. Mapping of the interface function at different time

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图 8 空气-R22激波与气柱相互作用的数值纹影图

Figure 8. Numerical schlieren diagram for the air-R22 shock-cylinder interaction problem

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表 1 水中气泡塌陷问题中状态方程参数及初始参数

Table 1. Equation of state parameters and the initial time data of an air cavity collapse in water

Material ρ/(kg·m^–3) p/Pa u/(m·s^–1) v/(m·s^–1) γ

Water (Post-shock) 1.325 1.915×10⁴ 68.52 0 4.4
Water (Pre-shock) 1 1 0 0 4.4
Air 0.001 1 0 0 1.4

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表 2 空气-R22气柱相互作用问题中的状态方程参数及初始参数

Table 2. Equation of state parameters and the initial time data of air-R22 shock-cylinder interaction

Material ρ/(kg·m^–3) p/MPa u/(m·s^–1) v/(m·s^–1) γ

Air (Post-shock) 1.686 0.159 –113.5 0 1.400
Air (Pre-shock) 1.225 0.101 0 0 1.400
R22 3.863 0.101 0 0 1.249

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