A sharp interface method for SPH
Update: 2016-02-02 13:30:34      Author: yangjuan@csrc.ac.cn

Many numerical methods have been developed to deal with the interface of multiphase flows. Volume of fluid (VOF)[1], level set method (LSM) [2], front tracking (FT) [3], and phase field (PF) [4]are famous numerical methods which have achieved great success in handling multiphase flows. These methods can be divided into two types: sharp interface method and diffuse interface method (DIM). SIM has sharp representation of interface and the material discontinuity is kept sharply. Geometrical calculations can be more accurate than DIM. Also, it is more convenient to deal with tangential force in SIM. In DIM, the interface is represented by a band of region with a few of numerical cells. The material discontinuity is smeared in this region. It is more convenient for DIM to simulate the interface coalescence or breakup.

Smoothed particle hydrodynamics (SPH) is a full Lagrangian meshless method [5]. The fluid is represented by a set of SPH particles. The flow variables are stored in these SPH particles. SPH has been developed to simulate fluid flows for more than twenty years. But accuracy is always a problem in SPH simulations.

In this work, a sharp interface method for SPH is developed to deal with the free interface, material discontinuity and physical jump conditions across the interface in two-phase flows. LSM is used to track the interface, and the interface is reconstructed explicitly based on it. The level set function is initially set to be the signed distance to the interface, and then evolves according to the level set equation. The ghost fluid method (GFM) is introduced to handle the discontinuity. The interface states are calculated by using of the jump conditions and are extended to the ghost fluid particles. The ghost fluid method helps to get smooth and stable calculation near the interface. All jump conditions in the normal and tangential directions are satisfied so that it can reflect the real physics better.

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Fig. 1. Scheme of sharp interface method for SPH.

Numerical tests show the accuracy and stability of our method. An oscillating cylinder test case is shown in Fig. 2. The 1st version is the one published in JCP. The 2nd version is the improved one with interface calculated via geometrical information of the SPH particles, which is more robust and gives better simulation results than the 1st version.

For more information on the 1st version, please see the paper: “A sharp interface method for SPH”, J. of Comput. Phys. 302 (2015). DOI: 10.1016/j.jcp.2015.09.015. The paper for the 2nd version is in preparation.

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Fig. 2. The contour (left) and periodic analysis (right) of the liquid cylinder oscillation case. The period shows good convergence when the SPH particle number increases, and the 2nd version shows better performance than the 1st version.

This research is supported by NSFC (Grant Nos. 91230203, 11202020).

References:

[1]. C. W. Hirt and B. D. Nichols, Volume of fluid (VOF) method for the dynamics of free boundaries, Journal of Computational Physics, 39 (1) (1981) 201-225.

[2] J. A. Sethian and P. Smereka, Level set methods for fluid interfaces, annual Review of Fluid Mechanics, 35 (2003) 341-372.

[3] G. Tryggvason, B. Bunner, A. Esmaeeli, D. Juric, N. Al-Rawahi, W. Tauber, J. Han, S. Nas and Y.-J. Jan, A Front-Tracking Method for the Computations of Multiphase Flow Journal of Computational Physics, 169 (2) (2001) 708-759.

[4] D. Jacqmin, Calculation of Two-Phase Navier-Stokes Flows Using Phase-Field Modeling, Journal of Computational Physics, 155 (1) (1999) 96-127.

[5] R. A. Gingold and J. J. Monaghan, Smoothed Particle Hydrodynamics - Theory and Application to Non-Spherical Stars, Monthly Notices of the Royal Astronomical Society, 181 (2) (1977) 375-389.


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