ECCOMAS 2024

A residual-based non-orthogonality correction for force-balanced unstructured Volume-of-Fluid methods

  • Liu, Jun (TU Darmstadt)
  • Maric, Tomislav (TU Darmstadt)

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Non-orthogonality errors in unstructured Finite Volume methods for simulating incompressible two-phase flows complicate the force-balanced discretization of the pressure gradient and the volume fraction gradients in the surface tension force and the gravity force in the discrete pressure Poisson equation. We show that the widespread view of applying the same explicit non-orthogonality correction for all gradient terms is not entirely sufficient to achieve force balance in segregated pressure-velocity solution algorithms. To ensure force balance, we introduce a straightforward residual-based control of the non-orthogonality correction, which deterministically sets the number of non-orthogonality corrections and removes it as a free parameter from the simulation. Our method is directly applicable to different unstructured finite-volume two-phase flow simulation methods as long as they discretize the one-field formulation of incompressible two-phase Navier-Stokes equations. We demonstrate force balance for the surface tension force and the gravity force near linear solver tolerance for an algebraic and a geometric Volume-of-Fluid method using the stationary droplet and stationary water column verification cases on polyhedral unstructured meshes with varying levels of non-orthogonality.