Weak and strong wall boundary procedures and convergence to steady-state of the Navier-Stokes equations

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• 作者：Jan Nordströ ; m^a ; ^{Jan.Nordstrom@liu.se} ; Sofia Eriksson^b ; Peter Eliasson^c
• 关键词：Navier&ndash ; Stokes ; Steady-state ; Boundary conditions ; Convergence ; Summation-by-parts
• 刊名：Journal of Computational Physics
• 出版年：2012
• 期刊代码：136_00219991
• 类别：cp
• 出版时间：20 May, 2012
• 卷：231
• 期：14
• 页码：4867-4884
• 文件大小：1998 K

摘要

We study the influence of different implementations of no-slip solid wall boundary conditions on the convergence to steady-state of the Navier-Stokes equations. The various approaches are investigated using the energy method and an eigenvalue analysis. It is shown that the weak implementation is superior and enhances the convergence to steady-state for coarse meshes. It is also demonstrated that all the stable approaches produce the same convergence rate as the mesh size goes to zero. The numerical results obtained by using a fully nonlinear finite volume solver support the theoretical findings from the linear analysis.