A residual-based non-orthogonality correction for force-balanced unstructured Volume-of-Fluid methods
arxiv(2024)
摘要
Non-orthogonality errors in unstructured Finite Volume methods for simulating
incompressible two-phase flows may break the force-balanced discretization. We
show that applying the same explicit non-orthogonality correction for all
gradient terms in the context of segregated solution algorithms is not
sufficient to achieve force balance. To ensure force balance, we introduce a
straightforward and deterministic residual-based control of the
non-orthogonality correction, which removes the number of non-orthogonality
corrections 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.
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