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Published 2009 | Published
Journal Article Open

Stable Fourth Order Stream-Function Methods for Incompressible Flows with Boundaries


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 noslip 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.

Additional Information

© 2009 Global Science Press. Received March 11, 2008; Revised version received May 3, 2008; Accepted August 6, 2008. Online 2009-4-17. The first author would like to acknowledge funding from NSF under grants DMS-0713670 and ACI-0204932. The second author would like to acknowledge funding from NSERC Canada that supported this work. Mathematics subject classification: 65M12, 76D05.

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Published - Hou2009p5090J_Comput_Math.pdf


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August 22, 2023
August 22, 2023