A mixed marker and level-set front-tracking approximation for multiphase flows simulations

This paper introduces a novel algorithm for interface tracking, utilizing a numerical approach that integrates marker and level-set tools. The method employs a cloud of markers to initialize, reconstruct, and move the two phases within a finite element unstructured mesh. Various algorithms are introduced to manage the marker location effectively and precisely define the geometric characteristics of the interface, including its normal and curvature. In each cell containing the front (“cut cell”), the interface reconstruction entails a best-fit quadratic level-set approximation of the existing markers, with the new markers repositioned at the zeros of the level-set function. A novelty of this paper is the introduction of exact quadrature rules applied within each cut cell to evaluate the embedded interface and subdomain integrals for capillary force and volume of fluid evaluation. The algorithm’s validity is substantiated through numerous kinematic and dynamic tests with square Cartesian, and unstructured triangular and quadrangular cells, and its performance is compared to the existing literature.