TY - JOUR
T1 - Stable Fourth-Order Stream-Function Methods for Incompressible Flows with Boundaries
JO - Journal of Computational Mathematics
VL - 4
SP - 441
EP - 458
PY - 2009
DA - 2009/08
SN - 27
DO - http://doi.org/10.4208/jcm.2009.27.4.012
UR - https://global-sci.org/intro/article_detail/jcm/8582.html
KW - Incompressible flow, Stream-function formulation, Finite difference methods.
AB - <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>