A conservative level-set method based on a posterior mass correction with preserving distance property for incompressible multiphase flows simulations

In this paper, a simple and efficient conservative level-set method for incompressible multiphase flow simulations is developed to address the conservation issue of the original level-set method. A mass correction procedure is proposed to enforce the level-set method's mass-conserving property, in which a small perturbation is introduced to the level-set field. With a derived analytical target equation, the perturbation value is efficiently determined by using a corresponding Newton–Raphson method. Unlike those existing mass correction procedures in previous research, the present mass correction can exactly preserve the signed distance property of the level-set function. As only algebraic operations are required for the present method, it is robust, efficient, and easy to implement, even in three-dimensional simulations. Moreover, we propose a delayed correction strategy to reduce the time cost of the proposed method, as the conservation errors can be well bounded during a small number of time steps. Various benchmark cases, including pure interface-evolution problems and multiphase flow problems, are computed to validate the present method. For all cases, the accuracy and the efficiency of the present method are compared to those of the original method. It is observed that, our delayed correction method merely introduces 5% and 1% extra time costs for the pure interface problems and the two-phase flow problems, respectively, compared to the original non-conservative method. The conservation error is reduced to the order of machine accuracy by using the present method, which indicates its potential applications in complex multiphase flow simulations.