  We present a novel Front-Tracking method, the Edge-Based Interface Tracking
(EBIT) method for multiphase flow simulations. In the EBIT method, the markers
are located on the grid edges and the interface can be reconstructed without
storing the connectivity of the markers. This feature makes the process of
marker addition or removal easier than in the traditional Front-Tracking
method. The EBIT method also allows almost automatic parallelization due to the
lack of explicit connectivity.
  In a previous journal article we have presented the kinematic part of the
EBIT method, that includes the algorithms for piecewise linear reconstruction
and advection of the interface. Here, we complete the presentation of the EBIT
method and combine the kinematic algorithm with a Navier--Stokes solver. A
circle fit is now implemented to improve the accuracy of mass conservation in
the reconstruction phase. Furthermore, to identify the reference phase and to
distinguish ambiguous topological configurations, we introduce a new feature:
the Color Vertex. For the coupling with the Navier--Stokes equations, we first
calculate volume fractions from the position of the markers and the Color
Vertex, then viscosity and density fields from the computed volume fractions
and finally surface tension stresses with the Height-Function method. In
addition, an automatic topology change algorithm is implemented into the EBIT
method, making it possible the simulation of more complex flows. The
two-dimensional version of the EBIT method has been implemented in the free
Basilisk platform, and validated with seven standard test cases: stagnation
flow, translation with uniform velocity, single vortex, Zalesak's disk,
capillary wave, Rayleigh-Taylor instability and rising bubble. The results are
compared with those obtained with the Volume-of-Fluid (VOF) method already
implemented in Basilisk.
