Hostname: page-component-78c5997874-g7gxr Total loading time: 0 Render date: 2024-11-10T15:23:29.915Z Has data issue: false hasContentIssue false
  • English
  • Français

A Numerical Method on Eulerian Grids for Two-Phase Compressible Flow

Part of: Optics, electromagnetic theory - General

Published online by Cambridge University Press:  27 January 2016

Yonghui Guo ,
Ruo Li  and
Chengbao Yao
Yonghui Guo
Affiliation:
Northwest Institute of Nuclear Technology, Xi'an 710024, China
Ruo Li*
Affiliation:
HEDPS & CAPT, LMAM & School of Mathematical Sciences, Peking University, Beijing 100871, China
Chengbao Yao
Affiliation:
School of Mathematical Sciences, Peking University, Beijing 100871, andNorthwest Institute of Nuclear Technology, Xi'an 710024, China
*
*Corresponding author. Email: gyh661012@163.com (Y. H. Guo), rli@math.pku.edu.cn (R. Li), yaocheng@pku.edu.cn (C. B. Yao)
Get access

Abstract

We develop a numerical method to simulate a two-phase compressible flow with sharp phase interface on Eulerian grids. The scheme makes use of a levelset to depict the phase interface numerically. The overall scheme is basically a finite volume scheme. By approximately solving a two-phase Riemann problem on the phase interface, the normal phase interface velocity and the pressure are obtained, which is used to update the phase interface and calculate the numerical flux between the flows of two different phases. We adopt an aggregation algorithm to build cell patches around the phase interface to remove the numerical instability due to the breakdown of the CFL constraint by the cell fragments given by the phase interface depicted using the levelset function. The proposed scheme can handle problems with tangential sliping on the phase interface, topological change of the phase interface and extreme contrast in material parameters in a natural way. Though the perfect conservation of the mass, momentum and energy in global is not achieved, it can be quantitatively identified in what extent the global conservation is spoiled. Some numerical examples are presented to validate the numerical method developed.

Keywords

Two-phase flowlevelsetRiemann problem

MSC classification

Secondary: 78A48: Composite media; random media
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 8 , Issue 2 , April 2016 , pp. 187 - 212
Copyright
Copyright © Global-Science Press 2016 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]Brackbill, J. U., Kothe, D. B., and Ruppel, H. M., FLIP: a low-dissipation, particle-in-cell method for fluid flow, Comput. Phys. Commun., 48(1) 91988), pp. 25–38.Google Scholar
[2]Di, Yana, Li, Ruo, Tang, Tao, and Zhang, Pingwen, Level set calculations for incompressible two-phase flows on a dynamically adaptive grid, J. Sci. Comput., 31(1-2) (2007), pp. 75–98.Google Scholar
[3]Enright, Douglas, Fedkiw, Ronald, Ferziger, Joel, and Mitchell, Ian, A hybrid particle level set method for improved interface capturing, J. Comput. Phys., 183(1) (2002), pp. 83–116.Google Scholar
[4]Hieber, Simone E and Koumoutsakos, Petros, A Lagrangian particle level set method, J. Comput. Phys., 210(1) (2005), pp. 342–367.CrossRefGoogle Scholar
[5]Koshizuka, Seiichi, Nobe, Atsushi, and Oka, Yoshiaki, Numerical analysis of breaking waves using the moving particle semi-implicit method, Int. J. Numer. Methods Fluids, 26(7) (1998), pp. 751–769.Google Scholar
[6]Koumoutsakos, Petros, Multiscale flow simulations using particles, Ann. Rev. Fluid Mech., 37 (2005), pp. 457–487.Google Scholar
[7]Monaghan, Joe J., Smoothed particle hydrodynamics, Reports Progress Phys., 68(8) (2005), pp. 1703.Google Scholar
[8]Noh, William F.and Woodward, Paul(Simple Line Interface Calculation). In Proceedings of the Fifth International Conference on Numerical Methods in Fluid Dynamics June 28–July 2, 1976, Twente University, Enschede, pp. 330–340, Springer, 1976Google Scholar
[9]Osher, Stanley and Fedkiw, Ronald P., Level set methods: an overview and some recent results, J. Comput. Phys., 169(2) (2001), pp. 463–502.Google Scholar
[10]Qiao, Dengjiang, An Introduction to Nuclear Explosion Physics, National Defence Industry Press (in Chinese), 2003.Google Scholar
[11]Rider, William J and Kothe, Douglas B, Stretching and tearing interface tracking methods, in AIAA Computational Fluid Dynamics Conference, 12th, and Open Forum, San Diego, CA, pp. 806–816, 1995.Google Scholar
[12]Sbalzarini, I. F., Walther, Jens Honore, Bergdorf, M., Hieber, S. E., Kotsalis, E. M., and Koumoutsakos, P., PPM-a highly efficient parallel particle-mesh libibrary for the simulation of continuum systems, J. Comput. Phys., 215(2) (2006), pp. 566–588.Google Scholar
[13]Scardovelli, Ruben and Zaleski, Stéphane, Direct numerical simulation of free-surface and interfacialflow, Ann. Rev. Fluid Mech., 31(1) (1999), pp. 567–603.Google Scholar
[14]Sethian, James A., Evolution, implementation, and application of level set and fast marching methods for advancing fronts, J. Comput. Phys., 169(2) (2001), pp. 503–555.Google Scholar
[15]Sussman, Mark, A second order coupled level set and volume-of-fluid method for computing growth and collapse of vapor bubbles, J. Comput. Phys., 187(1) (2003), pp. 110–136.Google Scholar
[16]Sussman, Mark, Smereka, Peter, and Osher, Stanley, A level set approach for computing solutions to incompressible two-phase flow, J. Comput. Phys., 114(1) (1994), pp. 146–159.Google Scholar
[17]Tryggvason, Grétar, Bunner, Bernard, Esmaeeli, Asgsghar, Juric, Damir, Al.-Rawahi, N., Tauber, W., Han, J., Nas, S., and Jan, Y. J., a front-tracking method for the computations of multiphase flow, J. Comput. Phys., 169(2) (2001), pp. 708–759.CrossRefGoogle Scholar
[18]Unverdi, S. O. and Tryggvason, G., A front-tracking method for viscous, incompressible, multi-fluid flows, J. Comput. Phys., 100(1) (1992), pp. 25–37.Google Scholar
[19]Walther, Jens Honore, Werder, T., Jaffe, R. L., and Koumoutsakos, P., Hydrodynamic properties of carbon canotubes, Phys. Rev. E, 69(6) (2004), pp. 062201.Google Scholar
[20]Han Young, Yoon, Koshizuka, Seiichi, and Oka, Yoshiaki, Direct calculation of bubble growth, departure, and rise in nucleate pool boiling, Int. J. Multiphase Flow, 27(2) (2001), pp. 277–298.Google Scholar