Balancing Forces in a Segregated Polyhedral Finite-Volume Solution of Single-Field Navier-Stokes Equations for Incompressible Two-Phase Flows

  • Maric, Tomislav (MMA, TU Darmstadt)

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An imbalance of forces at the fluid interface, caused by inconsistencies in the discretization of the pressure gradient and the surface tension force was a long standing source of instabilities in numerical solutions of the single-field formulation of Navier-Stokes equations for incompressible two-phase flows. A straightforward solution to this problem on equidistant meshes is to discretize the pressure gradient and the gradient of the phase indicator in the pressure equation using the same discretization scheme. However, achieving force balance in a segregated polyhedral finite volume discretization is more challenging, especially when the phase indicator is advected using the geometrical unstructured VOF method. The explicit correction of non-orthogonality errors causes a force imbalance. This type of force imbalance must be addressed to enable stable simulations of capillary flows in geometrically complex (engineering) systems. In this talk, we will analyze the root cause of the problem and suggest possible solutions.