A semi‐staggered finite volume approach applied to two‐ and three‐dimensional flow in channels with gradual expansions

Abstract

AbstractTwo‐ and three‐dimensional computations have been performed to study incompressible laminar flow of viscous fluids in symmetric channels with gradual expansions. The divergent form advective and viscous terms of Navier–Stokes equations are discretized by means of the UNIFAES scheme, which has been showing unpaired accuracy. Explicit time‐wise integration allows continuity to be imposed via the Poisson equation for the pressure, solved iteratively with several iterations per velocity step in order to ensure mass conservation throughout the transient regime. The proposed finite volume approach uses the semi‐staggered mesh structure, in which pressure is put at the center of the continuity cell and the velocity components at the cell vertexes. Comparative studies have shown this mesh to be highlighted by accuracy, in relation to the traditional, staggered and collocated meshes. Furthermore, it was observed that the semi‐staggered mesh allowed to treat a plane diverging channel in entirely regular fashion without losing accuracy, by appropriate choice of the aspect ratio of the numerical cell, providing geometrical flexibility that does not exist in more common meshes, such as staggered and collocated structures. The present proposal explored the geometric flexibility of the semi‐staggered mesh to solve with simplicity a relevant problem of a channel with gradual expansion. Overall, good agreement was observed against experimental and numerical results in the literature, therefore, it illustrates the capability of the semi‐staggered approach to easily handle flat surfaces nonparallel to the coordinates axes.