Comparative Study of UNIFAES and other Finite-Volume Schemes for the Discretization of Advective and Viscous Fluxes in Incompressible Navier-Stokes Equations, Using Various Mesh Structures

Abstract

The performance of the unified finite approaches exponential-type scheme (UNIFAES) for advective and diffusive transport equations, for the incompressible Navier-Stokes equations in primitive variables, is evaluated by comparison with the central differencing and the exponential scheme. Staggered, semistaggered, vertex collocated, and cell-center collocated meshes are considered. The Cartesian two-dimensional lid-driven cavity test problem is employed both in its traditional form with uniform lid velocity and in the regularized form without corner discontinuities. Richardson extrapolation is employed to produce reference results in the cases without prior precise reference solutions. The UNIFAES shows accuracy generally superior to the other schemes and stability even at the highest Reynolds numbers employed. This article also completes a previous comparative study of the performance of the mesh structures, generalizing the results there observed for higher Reynolds numbers and for schemes other than central differencing.

Comparative Study of the Accuracy of the Fundamental Mesh Structures for the Numerical Solution of Incompressible Navier-Stokes Equations in the Two-Dimensional Cavity Problem

“…Also, the direction of the errors of the semistaggered mesh in the regularized cavity problem, here called accelerating errors, suggests errors of dispersive type, which may lead to numerical instability, while the decelerating or diffusive types of errors present a stabilizing effect. No such instability was noticed in the present work, but some indications of it are presented in [33]. Furthermore, a slightly different picture of the accuracy of the meshes emerges in this study for other schemes and higher Reynolds numbers.…”

“…In order to minimize the errors other than those associated with the mesh structures, central differencing is used in the discretizations of the advective and viscous terms of the momentum equations, limiting the range of Reynolds numbers that can be investigated. This limitation is overcome in a companion article employing more stable schemes [33].…”

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

“…As depicted in Figure 1, adjacent to the walls the staggered mesh presents irregularly spaced tangential velocity component, and the collocated mesh presents all velocity components irregularly spaced, while the semi-staggered mesh is the unique regularly spaced mesh, besides the discarded vertex collocated approach. 28,41,42 Furthermore, the semi-staggered mesh can be regular not only along coordinate axis but also in inclined walls if the aspect ratio of the mesh can be appropriately chosen, being the unique mesh that can treat a plane diverging channel in entirely regular fashion. This feature is exploited in the present work by choosing the cell aspect ratio according to the opening angle of a channel expansion.…”

“…The above-mentioned mesh structures were subject to a comparative study employing the cavity flow problem. 28,41,42 The staggered mesh appeared as the most stable and robust, but relatively inaccurate. Cell center collocated mesh had better accuracy at refined grids, but a high Reynolds numbers it presented abrupt changes with refinement from inaccurate to accurate patterns.…”

An accurate discretization for an inhomogeneous transport equation with arbitrary coefficients and source

“…The third term appeared because the exact solution with a constant source in the control volume contains a linear term related to the source. Amongst these approaches is the UNIFAES scheme [13] [14] and the scheme adopted by Sheu et al [15]. In the latter a linear absorption term was also included.…”