Two-Level Stabilized Finite Volume Methods for the Stationary Navier-Stokes Equations

Abstract

AbstractIn this work, two-level stabilized finite volume formulations for the 2D steady Navier-Stokes equations are considered. These methods are based on the local Gauss integration technique and the lowest equal-order finite element pair. Moreover, the two-level stabilized finite volume methods involve solving one small Navier-Stokes problem on a coarse mesh with mesh size H, a large general Stokes problem for the Simple and Oseen two-level stabilized finite volume methods on the fine mesh with mesh size or a large general Stokes equations for the Newton two-level stabilized finite volume method on a fine mesh with mesh size . These methods we studied provide an approximate solution with the convergence rate of same order as the standard stabilized finite volume method, which involve solving one large nonlinear problem on a fine mesh with mesh size h. Hence, our methods can save a large amount of computational time.