Numerical assessment of finite volume schemes for incompressible viscous flows on non-staggered meshes

Performance of seven finite-volume differencing schemes for the advective and diffusive terms of two-dimensional transport equations was evaluated in two well-documented test problems employing non-staggered meshes. A new numerical error estimation procedure using Richardson’s extrapolation is proposed, called the common points extrapolation approach or CPE. The first test problem is the transport of an inert scalar through a parallel velocity field, whose exact solution is known and was used to determine the convergence rate of the tested schemes. Later, the exact solution was used as proof of concept of the proposed error estimation procedure. The second test problem is composed by two laminar flows in sudden expansions, which is modeled by continuity and Navier–Stokes equations, where the exact solution is unknown. Numerical solutions employ the primitive variables formulation using the semi-staggered mesh and the Poisson equation for pressure. In this test was shown how the common points extrapolation approach can be used for the estimation of numerical errors in non-theoretical test problems. Schemes considered are the classic references, central differencing (CDS) and first-order upwind (FOU), the polynomial schemes second-order upwind (SOU) and QUICK, and the exponential-type schemes simple exponential (EXP), LOADS and UNIFAES.