Long Time Numerical Solution of the Navier--Stokes Equations Based on a Sequential Regularization Formulation

Abstract. The sequential regularization method is a reformulation of the unsteady Navier-Stokes equations from the view point of constrained dynamical systems or approximate Helmholtz-Hodge projection. In this paper we study the long time behavior of the sequential regularization formulation. We give a uniform-in-time estimate between the solution of the reformulated system and that of the Navier-Stokes equations. We also conduct error analysis for the temporal discrete system and show that the error bound is independent of time. A couple of long time flow examples are computed to demonstrate this method.

• Type: Journal
• Year: 2008
• Where: SIAMSC
• Authors: Ping Lin, Jian-Guo Liu, Xiliang Lu
• Keywords: Navier-Stokes Equations, Sequential Regularization, Sequential Regularization Method, SIAMSC 2008