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A two-phase 2D model that combines the volume of fluid (VOF) method with implicit staggered finite volumes discretization of the Navier–Stokes equation is presented. Staggered finite volumes are developed on the basis of nonconforming Crouzeix–Raviart finite elements, where all components of the velocity lie in the middle of the element edges and the pressure degrees of freedom are found in the centers of mass of the elements. Staggered finite Volumes extend marker and cell (MAC) regular staggered grids to unstructured mesh. A linear saddle point problem, resulting from either the discretization or the Newton method, is solved for all unknown pressures and velocities. Interface is represented with spline interpolants which follow the VOF distribution. Adaptive mesh refinement is used to obtain a high level of uniform refining at the domain of dependence of the interface. The aligned grid is obtained by …