Interface treating methods for the gas-water multi-phase flows
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摘要: 针对不可压缩可压缩水/气多介质问题, 提出一种新的界面处理方法。在可压缩水/气界面处构造Riemann问题, 在水中设音速趋于无穷大, 求解Riemann问题得到不可压缩可压缩水/气界面处流体的准确流动状态; 然后以此状态结合GFM(ghost fluid method)方法分别为2种流体定义界面边界条件, 将两相流问题转化为单相流问题计算, 通过求解level set方程来跟踪界面的位置。对各种不同的界面边界条件定义方法进行了比较, 数值模拟结果表明算法能准确地捕捉各类间断的位置, 证明了算法的有效性和稳健性。Abstract: A new interface treating method is presented for the compressible-incompressible gas-water multi-phase flow.The Riemann problem is constructed at the compressible gas-water interface, and then solved according to the hypothesis that the sound speed tends to infinity in the water.The solution of Riemann problem provides the fluid states for compressible gas and incompressible water at the interface.Those states can then be used to define the interface boundary condition by coupling the ghost fluid method.The level set method is employed to track the interface.The numerical examples of one-dimension case are given in this paper, furthermore, several comparisons are made with other results to verify the algorithm.Numerical results show that the provided algorithm can capture the discontinuities accurately, which demonstrates the robustness and efficiency.
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Key words:
- mechanics of explosion /
- Riemann problem /
- ghost fluid method /
- level set /
- gas-water interface /
- multi-phase flows
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图 1 利用MGFM方法对气体定义界面边界条件
Figure 1. The definition of interface boundary condition for gas by MGFM method
图 2 利用RGFM方法对气体定义界面边界条件
Figure 2. The definition of interface boundary condition for gas by RGFM method
图 3 密度1 000 kg/m3的水在空气中向右运动时流场密度
Figure 3. Density profile of the water movement in air while water density is 1 000 kg/m3
图 4 密度1 000 kg/m3的水在空气中向右运动时流场速度
Figure 4. Velocity profile of the water movement in air while water density is 1 000 kg/m3
图 5 密度1 000 kg/m3的水在空气中向右运动时流场压力
Figure 5. Pressure profile of the water movement in air while water density is 1 000 kg/m3
图 7 密度10 kg/m3的水在空气中向右运动时流场密度
Figure 7. Density profile of the water movement in air while water density is 10 kg/m3
图 8 密度10 kg/m3的水在空气中向右运动时流场速度
Figure 8. Velocity profile of the water movement in air while water density is 10 kg/m3
图 9 密度10 kg/m3的水在空气中向右运动时流场压力
Figure 9. Pressure profile of the water movement in air while water density is 10 kg/m3
图 11 水密度1 000 kg/m3时激波与水/气界面相互作用后的流场密度
Figure 11. Density profile of shock impact with water-gas interface while water density is 1 000 kg/m3
图 12 水密度1 000 kg/m3时激波与水/气界面相互作用后的流场速度
Figure 12. Velocity profile of shock impact with water-gas interface while water density is 1 000 kg/m3
图 13 水密度1 000 kg/m3时激波与水/气界面相互作用后的流场压力
Figure 13. Pressure profile of shock impact with water-gas interface while water density is 1 000 kg/m3
图 15 水密度10 kg/m3时激波与水/气界面相互作用后的流场密度
Figure 15. Density profile of shock impact with water-gas interface while water density is 10 kg/m3
图 16 水密度10 kg/m3时激波与水/气界面相互作用后的流场速度
Figure 16. Velocity profile of shock impact with water-gas interface while water density is 10 kg/m3
图 17 水密度10 kg/m3时激波与水/气界面相互作用后的流场压力
Figure 17. Pressure profile of shock impact with water-gas interface while water density is 10 kg/m3
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[1] Caiden R, Fedkiw R P, Anderson C. A numerical method for two-phase flow consisting of separate compressible and incompressible regionsg[J]. Journal of Computational Physics, 2001, 166(1): 1-27. [2] Fedkiw R P, Aslam T, Merriman B, et al. A non-oscillatory Eulerian approach to interfaces in multimaterial flows: The ghost fluid method[J]. Journal of Computational Physics, 1999, 152(2): 457-492. [3] Liu T G, Khoo B C, Yeo K S. Ghost fluid method for strong shock impacting on material interface[J]. Journal of Computational Physics, 2003, 190(2): 651-681. [4] Liu T G, Khoo B C, Wang C W. The ghost fluid method for gas-water simulation[J]. Journal of Computational Physics, 2005, 204(1): 193-221. [5] Wang C W, Liu T G, Khoo B C. A real ghost fluid method for the simulation of multimedium compressible flow[J]. SIAM Journal on Scientific Computing, 2006, 28(1): 278-302. [6] 王春武, 赵宁.基于求解Riemann问题的界面处理方法[J].计算物理, 2006, 22(4): 306-310.Wang Chun-wu, Zhao Ning. An interface treating method based on Riemann problems[J]. Chinese Journal of Computational Physics, 2006, 22(4): 306-310. [7] Agemi R. The incompressible limit of compressible fluid motion in a bounded domain[C]∥Proceedings of the Japan Academy Series A: Mathematical Sciences. 1981. [8] Steve S. The compressible Euler equations in a bounded domain: Existence of solutions and the incompressible limit[J]. Communications in Mathematical Physics, 1986, 104(1): 49-75. [9] Asano K. On the incompressible limit of the compressible Euler equation[J]. Japan Journal of Applied Mathematics, 1987, 4(3): 455-488. [10] Jiang G S, Shu C W. Efficient implementation of weighted ENO schemes[J]. Journal of Computational Physics, 1996, 126(1): 202-228. http://www.sciencedirect.com/science/article/pii/S0021999196901308 -
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