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Numerical computation of three-dimensional incompressible viscous flows in the primitive variable form by local multiquadric differential quadrature method. (English) Zbl 1222.76072

Summary: The local multi-quadric differential quadrature (LMQDQ) method is applied on three-dimensional incompressible flow problems. The LMQDQ method is among the newly proposed mesh-free methods. Unlike the traditional differential quadrature (DQ) method, the weighting coefficients of LMQDQ method are determined by using the radial basis functions as trial functions instead of high-order polynomials. The main concern of this paper is to discuss the effectiveness of using LMQDQ method to solve 3D incompressible Navier-Stokes equations in the primitive-variable form. Three-dimensional lid-driven cavity flow problem with Reynolds numbers of 100, 400 and 1000 was chosen as a test case to validate the LMQDQ method. The computed velocity profiles along the vertical and horizontal centre lines are given and compared with available data in the literature.

MSC:

76M25 Other numerical methods (fluid mechanics) (MSC2010)
76D05 Navier-Stokes equations for incompressible viscous fluids
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