An interface capturing approach based on a level set function for simulating transient two-phase viscous incompressible flows is applied in this paper. A narrow-band signed distance function is adopted to indicate the phase fields and the interface. The multiphase flow is numerically solved by three stages with finite element method (FEM):

  • solving a two-fluid Navier-Stokes equation over the whole domain;

  • transporting the level set function with the obtained velocity field;

  • the level set function correction through a renormalization with continuous penalization which preserves the thickness of the interface.

In this paper, the classical 3D Dam-break benchmark cases are tested for verification, which yielded good agreement with the experimental data.


Free surface flows have showed the importance in naval technology and offshore engineering, such as sloshing in the tank, wave generated by ship's motion, wave-structure interaction, and so on. Performing accurate, robust and efficient simulations of the free surface flows has been the object of numerous research projects for several decades. The dam-break problem is a critical part in the design and management of hydraulic engineering, which has been studied both experimentally and numerically. Martin and Moyce conducted an experimental study on this problem in the early 1950s. Then, numerous researchers simulated dambreak flow by kinds of numerical methods, which make it a classical benchmark. Interface tracking methods can be purely Lagrangian, as particle methods, or they are developed as Arbitrary Lagrangian-Eulerian (ALE) approaches. The most widely used particle methods are Smoothed Particle Hydrodynamics (SPH) and Moving Particle Semi-Implicit (MPS). Zhang et al. (2010) have done the comparative study of SPH and MPS methods for numerical simulations of 2D dam-break problems. Later, Zhang et al. (2011) have applied a modified MPS method in 3D dam-break problem, showing good agreement with experimental data.

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