Application of Local MQ-DQ Method to Solve 3D Incompressible Viscous Flows with Curved Boundary
Y.Y. Shan; C. Shu; and Z.L. Lu

Source CMES: Computer Modeling in Engineering & Sciences, Vol. 25, No. 2, pp. 99-114, 2008
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Keywords Local MQ-DQ method; Error estimate; Flow past a sphere
Abstract The local multiquadric-based differential quadrature (MQ-DQ) method proposed by [Shu, Ding, and Yeo (2003)] is a natural mesh-free approach for derivative approximation, which is easy to be implemented to solve problems with curved boundary. Previously, it has been well tested for the two-dimensional (2D) case. In this work, this mesh-free method was extended to simulate fluid flow problems with curved boundary in three-dimensional (3D) space. The main concern of this work is to numerically study the performance of the 3D local MQ-DQ method and demonstrate its capability and flexibility for simulation of 3D incompressible fluid flows with curved boundary. Fractional step method was adopted for the solution of Navier-Stokes (N-S) equations in the primitive-variable form. Flow past a sphere with various Reynolds numbers was chosen as a test case to validate the 3D local MQ-DQ method. The computed solution was compared well with available data in the literature. The numerical solution shows that the local MQ-DQ method can be applied to solve incompressible viscous flow problems with curved boundary in 3D space effectively.
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