Nonorthogonality Correction Method for a Two-Phase Semiimplicit Algorithm on a Polyhedral Unstructured Mesh

Nonorthogonality is often encountered in structured or unstructured mesh generation for computational fluid dynamics (CFD). A flow solution from CFD can degenerate because of mesh nonorthogonality. Sometimes, it is difficult to obtain a converged solution because of a numerical instability originating from a nonorthogonal mesh, especially in the case of a two-phase flow analysis. In this study, a method for nonorthogonality correction of a pressure-correction equation is proposed for application to a two-phase implicit continuous Eulerian (ICE) algorithm. In the case of a two-phase flow with buoyant force, a pressure gradient must be carefully reconstructed. A density-weighted interpolation of the pressure can be used for the pressure gradient, but it may generate an erroneous solution. Effort was devoted to improve the method and implement it for a general polyhedral mesh. The methods are implemented in the CUPID code and tested by solving conceptual two-phase flow problems.