A numerical method for interface reconstruction of triple points within a volume tracking algorithm

A numerical method for the reconstruction of interfaces in finite volume schemes for multiphase flows is presented. The computation of the triple-point at the intersection of three materials in two dimensions of space is addressed. The determination of the normal vectors between pairs of materials is obtained with a finite element approximation. A numerical method for the localization of a triple-point is described as the minimum of a constrained minimization problem inside an interfacial cell of the discretization. For given volume fractions of materials in the cell, an interior-point/Newton method is used for the reconstruction of the local geometry and the localization of the triple-point. Initialization of the Newton method is performed with a derivative-free algorithm. Numerical results are presented for static and pure advection cases to illustrate the efficiency and robustness of the algorithm.