An efficacy algorithm for the two dimensional steady Navier-Stokes equations by multi-grid scheme

Toni Sayah (1)

1 FS - Faculté des sciences-USJ

In this paper, we propose a multi-grid algorithm for solving the Navier-Stokes equations and we analyze its convergence. The proposed method consists of multi-level grids, where in the first one (the very coarse mesh h0 = H) we solve one small nonlinear system of discrete Navier-Stokes equations, then, in every intermediate mesh (h_i =(h_{i-1}^2 = H^{2i} ) we solve two linear problems and in the last one (the very fine mesh h_n = H_{2n}) we solve one linear system. Moreover, the algorithm produces a numerical solution with an optimal asymptotic error estimate with respect to h =h_n. Finally, we give some numerical illustrations showing the efficiency of the new multi-grid algorithm.

Mots clés: Multi-grid method; Navier-Stokes

Domaines: Analyse numérique [math.NA]

Toni Sayah. An efficacy algorithm for the two dimensional steady Navier-Stokes equations by multi-grid scheme. 2011. ⟨hal-00588930⟩