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

作     者：Thomas Y.Hou BrianR.Wetton 

作者机构：Department of Applied and Computational MathematicsCalifornia Institute of TechnologyPasadenaCA91125 USA Department of MathematicsUniversity of British ColumbiaVancouverBCV6T 1Z2Canada 

出 版 物：《Journal of Computational Mathematics》 (计算数学（英文）)

年 卷 期：2009年第27卷第4期

页      面：441-458页

核心收录：

学科分类：080704[工学-流体机械及工程] 080103[工学-流体力学] 08[工学] 0807[工学-动力工程及工程热物理] 0714[理学-统计学（可授理学、经济学学位）] 0701[理学-数学] 0812[工学-计算机科学与技术（可授工学、理学学位）] 0801[工学-力学（可授工学、理学学位）] 

基　　金：funding from NSF under grants DMS-0713670 and ACI-0204932 funding from NSERC Canada that supported this work 

主　　题：Incompressible flow Stream-function formulation Finite difference methods. 

摘      要：Fourth-order stream-function methods are proposed for the time dependent, incom- pressible 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.