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| The two-dimensional (2D) lid-driven cavity flow is simulated by applying the ordinary differential quadrature (DQ) method to solve the incompressible Navier-Stokes equations in stream function-vorticity form. There are two boundary conditions, one Dirichlet and one Neumann, for the stream function at each boundary though its governing equation is just second-order. Analysis on this over-specified problem is carried out, based on which a new method is proposed to implement these boundary conditions: the Neumann condition is just considered in the vorticity equation while only the Dirichlet condition is applied in the stream function equation. Availability of this method is verified by comparing its numerical results with benchmark data. Two other methods, the One-layer approach and the Two-layer approach, introduced by Shu and Xue (1998) are also shown as a contrast, and detailed formulations are repeated especially for the One-layer approach to reveal its underlying problem: this method is sensitive to the parity of grid numbers in two directions. Comparison between the present method and the Two-layer approach indicates that the former is more convenient to be used in practice for it avoiding the over-specified problem, and also more accurate, while the latter is relatively more efficient. |
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| Keywords:differential quadrature; stream function-vorticity equations; 2D lid-driven cavity flow; over-specified boundary conditions; multiple boundary conditions; incompressible |
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