A face-area-weighted ‘centroid’ formula for finite-volume method that improves skewness and convergence on triangular grids

Abstract

This paper proposes a face-area-weighted ‘centroid’ as a superior alternative to the geometric centroid for defining a local origin in a cell-centered finite-volume method on triangular grids. It is demonstrated theoretically and numerically that the face-area-weighted ‘centroid’ can reduce grid skewness and improve iterative convergence for triangular grids. It is also shown that source terms do not have to be integrated over a cell and can be evaluated simply at the local origin without losing the design order of accuracy. Numerical results demonstrate that the face-area-weighted ‘centroid’ improves iterative convergence of an implicit defect-correction second-order finite-volume solver for inviscid and viscous flow problems on regular and irregular triangular grids.