On improving mass-conservation properties of the hybrid particle-level-set method

For the computation of multi-phase flows level-set methods are an attractive alternative to volume-of-fluid or front-tracking approaches. For improving their accuracy and efficiency the hybrid particle-level-set modification was proposed by Enright et al. [Enright D, Fedkiw R, Ferziger J, Mitchell I. A hybrid particle-level-set method for improved interface capturing. J Comput Phys 2002;183:83–116]. In actual applications the overall properties of a level-set method, such as mass conservation, are strongly affected by discretization schemes and algorithmic details. In this paper we address these issues with the objective of determining the optimum alternatives for the purpose of direct numerical simulation of dispersed-droplet flows. We evaluate different discretization schemes for curvature and unit normal vector at the interface. Another issue is the particular formulation of the reinitialization of the level-set function which significantly affects the quality of computational results. Different approaches employing higher-order schemes for discretization, supplemented either by a correction step using marker particles (Enright et al., 2002) or by additional constraints [Sussman M, Almgren AS, Bell JB, Colella P, Howell LH, Welcome ML. An adaptive level set approach for incompressible two-phase flows. J Comput Phys 1999;148:81–124] are analyzed. Different parameter choices for the hybrid particle-level-set method are evaluated with the purpose of increasing the efficiency of the method. Aiming at large-scale computations we find that in comparison with pure level-set methods the hybrid particle-level-set method exhibits better mass-conservation properties, especially in the case of marginally resolved interfaces.