full
search.png

Search

close.png

Cancel

arrow
Volume 27, Issue 4
Stable Fourth-Order Stream-Function Methods for Incompressible Flows with Boundaries

Thomas Y. Hou & Brian R. Wetton

DOI: 10.4208/jcm.2009.27.4.012

J. Comp. Math., 27 (2009), pp. 441-458.

Published online: 2009-08

Preview Full PDF 2401 25672

Cited by

google scholar semantic scholar
Export citation
  • Abstract

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.

  • Keywords

Incompressible flow, Stream-function formulation, Finite difference methods.

  • AMS Subject Headings

65M12, 76D05.

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • BibTex
  • RIS
  • TXT
@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 = {

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.

}, 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} }
TY - JOUR T1 - Stable Fourth-Order Stream-Function Methods for Incompressible Flows with Boundaries AU - Thomas Y. Hou & Brian R. Wetton 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 -

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.

Thomas Y. Hou and Brian R. Wetton. (2009). Stable Fourth-Order Stream-Function Methods for Incompressible Flows with Boundaries. Journal of Computational Mathematics. 27 (4). 441-458. doi:10.4208/jcm.2009.27.4.012
Copy to clipboard
BibteX RIS TXT
The citation has been copied to your clipboard