3D two phase flows numerical simulations by SL‐VOF method

Abstract

SUMMARYThis paper describes the development of a semi-Lagrangian computational method for simulating complex 3D two phase ows. The Navier-Stokes equations are solved separately in both uids using a robust pseudo-compressibility method able to deal with high density ratio. The interface tracking is achieved by the segment Lagrangian volume of uid (SL-VOF) method. The 2D SL-VOF method using the concepts of VOF, piecewise linear interface calculation (PLIC) and Lagrangian advection of the interface is herein extended to 3D ows. Three di erent test cases of SL-VOF 3D are presented for validation and comparison either with 2D ows or with other numerical methods. A good agreement is observed in each case.

Numerical simulations of wave breaking

“…It is possible that the 3D effects become more and more important after the reconnection. The current power of personal computers is not sufficient to envisage precise 3D computations (for a recent attempt, see [2,3,24]). Recall that these numerical simulations can be interesting for the calibrating of empirical models in coastal engineering.…”

“…Hence, a coupled approach was recently proposed, for both 2D and 3D problems, in which wave generation and shoaling is simulated in a BEM-NWT up to a point close to breaking, and a VOF model is initialized using results of the BEM model, to pursue computations beyond breaking over a finely discretized grid. Wave breaking and post-breaking were thus computed in the VOF model [2,3,18,22].…”

Numerical Modeling and Experimental Validation of Free Surface Flow Problems

“…In 2D, the strategy combines the fluid fraction from VOF [104] and the linear reconstruction of the interface from PLIC together with a Lagrangian advection of the segments that define the interface, without surface tension. The SL-VOF was later extended to 3D cases by Biausser et al [27] and, coupled with a boundary integral element method with the aim of decreasing the computational costs [26].…”

A new volume of fluid method in three dimensions—Part II: Piecewise‐planar interface reconstruction with cubic‐Bézier fit

“…In the PLIC reconstruction method of Youngs [4] (see also [27,28]), the interface is reconstructed in each cell as a plane n·x+C = 0, in which the vector normal to the interface is obtained from the gradient of the volume fraction function, ∇F. A finite-difference formula is used to obtain the gradient of F at each corner of the cell.…”