Spectral Direction Splitting Schemes for the Incompressible Navier-Stokes Equations
Lizhen Chen 1, Jie Shen 2, Chuanju Xu 1*1 School of Mathematical Sciences, Xiamen University, 361005 Xiamen, China.
2 School of Mathematical Sciences, Xiamen University, 361005 Xiamen, China and Department of Mathematics, Purdue University, West Lafayette, IN, 47907, USA.
Received 19 April 2011; Accepted (in revised version) 24 May 2011
Available online 27 July 2011
We propose and analyze spectral direction splitting schemes for the incompressible Navier-Stokes equations. The schemes combine a Legendre-spectral method for the spatial discretization and a pressure-stabilization/direction splitting scheme for the temporal discretization, leading to a sequence of one-dimensional elliptic equations at each time step while preserving the same order of accuracy as the usual pressure-stabilization schemes. We prove that these schemes are unconditionally stable, and present numerical results which demonstrate the stability, accuracy, and efficiency of the proposed methods.
Key words: Navier-Stokes equations, projection method, direction splitting, spectral methods.
Email: email@example.com (C. Xu)