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.

在使用非交错网格的两个有据可查的测试问题中评估了二维传输方程的平流项和扩散项的七种有限体积差分方案的性能。提出了一种使用理查森外推法的新数值误差估计程序，称为公共点外推法或 CPE。第一个测试问题是惰性标量通过平行速度场的传输，其精确解是已知的，并用于确定测试方案的收敛速度。后来，精确解被用作所提出的误差估计程序的概念证明。第二个测试问题由两个突然膨胀的层流组成，由连续性和 Navier-Stokes 方程建模，其中精确解未知。数值解采用原始变量公式，使用半交错网格和压力泊松方程。在这个测试中，展示了公共点外推方法如何用于估计非理论测试问题中的数值误差。考虑的方案是经典参考、中心差分 (CDS) 和一阶逆风 (FOU)、多项式方案二阶逆风 (SOU) 和 QUICK，以及指数型方案简单指数 (EXP)、LOADS 和 UNIFAES。