A two-grid algorithm based on Newton iteration for the stream function form of the Navier-Stokes equations

作者：Shao Xin-ping^*; Han Dan-fu

来源：Applied Mathematics-A Journal of Chinese Universities Series B, 2011, 26(3): 368-378.

DOI：10.1007/s11766-011-2698-2

• Two-grid algorithm
• Navier-Stokes equations
• Stream function form
• Reynolds number
• Newton iteration

In this paper, we propose a two-grid algorithm for solving the stream function formulation of the stationary Navier-Stokes equations. The algorithm is constructed by reducing the original system to one small, nonlinear system on the coarse mesh space and two similar linear systems (with same stiffness matrix but different right-hand side) on the fine mesh space. The convergence analysis and error estimation of the algorithm are given for the case of conforming elements. Furthermore, the algorithm produces a numerical solution with the optimal asymptotic H (2)-error. Finally, we give a numerical illustration to demonstrate the effectiveness of the two-grid algorithm for solving the Navier-Stokes equations.

• 出版日期2011-9
• 单位浙江大学