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.

The authors express their gratitude for the support, in terms of a doctoral thesis grant, from CNPq, the Brazilian National Council for Scientific and Technological Development.