We investigate viscous boundary layers of the plane-parallel flow, governed by the stationary Navier–Stokes equations under a certain symmetry. Following the analysis in Gie et al. (Annales de l’Institut Henri Poincaré C. Analyse Non Linéaire, 2018), we first construct the so-called corrector, which is an analytic approximation of the velocity vector field near the boundary. Then, by embedding the corrector function into the classical Finite Volume schemes, we construct the semi-analytic enriched Finite Volume schemes for the plane-parallel flow, and numerically verify that our new enriched schemes reduce significantly the computational error of classical schemes especially near the boundary, and hence produce more accurate approximations without introducing any finer mesh near the boundary.

我们研究在一定对称性下由平稳的Navier–Stokes方程控制的平面平行流的粘性边界层。根据吉等人的分析。（Annales de l'Institut HenriPoincaréC.Analyze NonLinéaire，2018），我们首先构造了所谓的校正器，它是边界附近速度矢量场的解析近似。然后，通过将校正函数嵌入经典有限体积方案中，我们构造了平面平行流的半解析富集有限体积方案，并数值验证了我们的新富集方案显着减少了经典方案的计算误差，尤其是在接近边界，因此可以产生更精确的近似值，而无需在边界附近引入任何更精细的网格。