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Two-phase flows on interface refined grids modeled with VOF, staggered finite volumes, and spline interpolants. (English) Zbl 1030.76035
From the summary: We present a two-phase two-dimensional model that combines the volume-of-fluid (VOF) method with implicit staggered finite volume discretization of Navier-Stokes equations. 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 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 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. Using the proposed numerical techniques, we analyze single bubble rise.

76M12 Finite volume methods applied to problems in fluid mechanics
76M25 Other numerical methods (fluid mechanics) (MSC2010)
76T10 Liquid-gas two-phase flows, bubbly flows
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