CLSVOF as a fast and mass-conserving extension of the level-set method for the simulation of two-phase flow problems

ABSTRACT

The modeling of two-phase flows in computational fluid dynamics is still an area of active research. One popular method is the coupling of level-set and volume-of-fluid (CLSVOF), which benefits from the advantages of both approaches and results in improved mass conservation while retaining the straightforward computation of the curvature and the surface normal. Despite its popularity, details on the involved complex computational algorithms are hard to find and if found, they are mostly fragmented and inaccurate. In contrast, this article can be used as a comprehensive guide for an implementation of CLSVOF into the existing level-set Navier–Stokes solvers on Cartesian grids in three dimensions.

Notes

¹This definition of x_v can be understood as follows (cf. Figure 7): If (i′, j′, k′) is a direct neighbor of (i, j, k) (e.g. i′ = i + 1, j = j, k = k), then l = max (−1, min(1, i + 1 − i)) = max(−1, 1) = 1, m = max(−1, min(1, j − j)) = 0 and n = 0 so that , which is a face center of cell (i, j, k). If (i′, j′, k′) is a diagonal neighbor (e.g. i′ = i + 1, j = j + 1, k = k), then l = 1, j = 1, k = 0 and , which is a face corner.

²See Eq. (31) for the definition of the signed distance of a point p to a plane. This distance is positive, if p lies on the same side of the plane towards which the unit normal points and negative otherwise.

³Here, we define the x_f-face of cell (i, j, k) as

and we define the other faces analogously.

⁴However, the CLSVOF code cannot yet deal with anisotropies which is due to our present implementation – not the method itself.

⁵Note that our CLSVOF method is an essential yet still basic tool. Several enhancements such as unsplit advection [43], increased accuracy by higher order interface reconstruction [44] or even a completion by the CLSMOF method [18] are possible. All of these, however, presuppose a thorough understanding and implementation of the basics of the CLSVOF method in the first place which we provide in this article.