The localized differential quadrature method for two-dimensional stream function formulation of Navier-Stokes equations
Resource
Engineering Analysis with Boundary Elements, 35(11), 1190-1203
Journal
Engineering Analysis with Boundary Elements
Journal Volume
35
Journal Issue
11
Pages
1190-1203
Date Issued
2011
Date
2011
Author(s)
Tsai, C.H.
Young, D.L.
Hsiang, C.C.
Abstract
Localized differential quadrature (LDQ) method is employed to solve two-dimensional stream function formulation of incompressible NavierStokes equations. Being developed by introducing the localization concept to the general differential quadrature (GDQ) method, the employment of LDQ method becomes efficient and flexible, especially for the simulations of large scale computations. By introducing the Lagrange stream function to vorticity transport equation, the governing equation - the fourth-order partial differential equation (PDE) - is derived. To stably obtain the solutions of the fourth-order PDE, a fictitious point method is included to treat the boundary conditions. To examine the present scheme, two different types of classic benchmark fluid flow problems are proposed, including driven cavity flow problems and backward-facing step flow problems. The good agreement of solutions demonstrate the robustness and feasibility of the proposed scheme. Conclusively, the LDQ method is sufficient and appropriate enough to simulate the solutions of stream function formulation of NavierStokes equations with various Reynolds numbers. © 2011 Elsevier Ltd. All rights reserved.
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Type
journal article
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