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

陈芳, 李平, 刘坤, 柏劲松, 林健宇, 季路成. 基于PPM的界面压缩方法研究[J]. 高压物理学报, 2019, 33(5): 052302. doi: 10.11858/gywlxb.20180663
引用本文: 陈芳, 李平, 刘坤, 柏劲松, 林健宇, 季路成. 基于PPM的界面压缩方法研究[J]. 高压物理学报, 2019, 33(5): 052302. doi: 10.11858/gywlxb.20180663
CHEN Fang, LI Ping, LIU Kun, BAI Jingsong, LIN Jianyu, JI Lucheng. Interface Compression Technique in PPM[J]. Chinese Journal of High Pressure Physics, 2019, 33(5): 052302. doi: 10.11858/gywlxb.20180663
Citation: CHEN Fang, LI Ping, LIU Kun, BAI Jingsong, LIN Jianyu, JI Lucheng. Interface Compression Technique in PPM[J]. Chinese Journal of High Pressure Physics, 2019, 33(5): 052302. doi: 10.11858/gywlxb.20180663

基于PPM的界面压缩方法研究

doi: 10.11858/gywlxb.20180663
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

Interface Compression Technique in PPM

  • 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。

     

  • 图  一维纯对流问题

    Figure  1.  Solution of the one-dimensional advection test

    图  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)

    图  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)

    图  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 ${\Delta x =\Delta y = 0.006\;25}$)

    图  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

    图  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)

    图  不同时刻的界面分布

    Figure  7.  Mapping of the interface function at different time

    图  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

    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

    Materialρ/(kg·m–3)p/Pau/(m·s–1)v/(m·s–1)γ
    Water (Post-shock)1.3251.915×10468.5204.4
    Water (Pre-shock)11004.4
    Air0.0011001.4
    下载: 导出CSV

    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

    Materialρ/(kg·m–3)p/MPau/(m·s–1)v/(m·s–1)γ
    Air (Post-shock)1.6860.159–113.501.400
    Air (Pre-shock)1.2250.101001.400
    R223.8630.101001.249
    下载: 导出CSV
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  • 收稿日期:  2018-10-18
  • 修回日期:  2018-11-16

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