@Article{JCM-27-441,
author = {Thomas Y. Hou and Brian R. Wetton},
title = {Stable Fourth-Order Stream-Function Methods for Incompressible Flows with Boundaries},
journal = {Journal of Computational Mathematics},
year = {2009},
volume = {27},
number = {4},
pages = {441--458},
abstract = {<p style="text-align: justify;">Fourth-order stream-function methods are proposed for the time dependent, incompressible Navier-Stokes and Boussinesq equations. Wide difference stencils are used instead of compact ones and the boundary terms are handled by extrapolating the stream-function values inside the computational domain to grid points outside, up to fourth-order in the no-slip condition. Formal error analysis is done for a simple model problem, showing that this extrapolation introduces numerical boundary layers at fifth-order in the stream-function. The fourth-order convergence in velocity of the proposed method for the full problem is shown numerically.</p>},
issn = {1991-7139},
doi = {https://doi.org/10.4208/jcm.2009.27.4.012},
url = {http://global-sci.org/intro/article_detail/jcm/8582.html}
}