Two-level discretization of the Navier-Stokes equations with r-Laplacian subgridscale viscosity



The r-Laplacian has played an important role in the development of computationally efficient models for applications, such as numerical simulation of turbulent flows. In this article, we examine two-level finite element approximation schemes applied to the Navier-Stokes equations with r-Laplacian subgridscale viscosity, where r is the order of the power-law artificial viscosity term. In the two-level algorithm, the solution to the fully nonlinear coarse mesh problem is utilized in a single-step linear fine mesh problem. When modeling parameters are chosen appropriately, the error in the two-level algorithm is comparable to the error in solving the fully nonlinear problem on the fine mesh. We provide rigorous numerical analysis of the two-level approximation scheme and derive scalings which vary based on the coefficient r, coarse mesh size H, fine mesh size h, and filter radius δ. We also investigate the two-level algorithm in several computational settings, including the 3D numerical simulation of flow past a backward-facing step at Reynolds number Re = 5100. In all numerical tests, the two-level algorithm was proven to achieve the same order of accuracy as the standard one-level algorithm, at a fraction of the computational cost. © 2011 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2011