STABLE FOURTH-ORDER STREAM-FUNCTION METHODS FOR INCOMPRESSIBLE FLOWS WITH BOUNDARIES

• 来源期刊: 计算数学（英文版）
• 关键词: Incompressible flow Stream-function formulation Finite difference methods
• 年，卷（期）: 2009,（4）
• 页码范围: 441-458
• 页数: 18页
• 语种: 英文
• DOI: 10.4208/jcm.2009.27.4.012

摘要

Fourth-order stream-function methods are proposed for the time dependent, incom-pressible Navier-Stokes and Bonssinesq 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.