A residual-based non-orthogonality correction for force-balanced unstructured Volume-of-Fluid methods
Abstract
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.
Keywords
Cite
@article{arxiv.2402.04043,
title = {A residual-based non-orthogonality correction for force-balanced unstructured Volume-of-Fluid methods},
author = {Jun Liu and Tobias Tolle and Tomislav Maric},
journal= {arXiv preprint arXiv:2402.04043},
year = {2024}
}