New Treatment of Nonorthogonal Terms in the Pressure-Correction Equation

Study of the effect of the non-orthogonality for non-staggered grids—the theory

“…The two-dimensional lid-driven cavity flows are selected for the study. This problem has been studied by Peric [10] and Cho and Chung [11]. Their work will be described in a companion article [12].…”

A coupled finite volume method for the computational modelling of mould filling in very complex geometries

“…However, omission or simplification of these terms can introduce stability problems into the solution process and lead to difficulties with convergence on highly distorted meshes. Since in complex geometries it is often not possible to have a good quality mesh over the entire domain, many authors have sought to address this problem [18][19][20].…”

Study of the effect of the non-orthogonality for non-staggered grids—The results

“…But the range of the pressure underrelaxation factor gets narrow much faster if the simplified pressure-correction equation is used than that if the full one is used. Recently, Cho and Chung [6] proposed a new treatment method for non-orthogonal terms in the pressure-correction equation in order to enlarge the ranges of the values of the pressure underrelaxation factor for convergence. In this new treatment, the non-orthogonal terms in the full pressure-correction equation are decomposed into explicit and implicit terms and five nodes for 2D flows and seven nodes for 3D flows are used in the coefficient matrix for the pressure-correction equation.…”

“…Although this treatment is superior to the simplified treatment if the grids are significantly non-orthogonal, its pressure-correction equation is more complex than the simplified one. In both studies [5,6], the SIMPLE algorithm was used to solve the governing equations on 20× 20 control volumes or grids with Re= 100. The analyses in [5,6], in the investigators' words, are valid for both staggered and non-staggered grid arrangements.…”