Abstract
The local multiquadric-based differ- ential quadrature (MQ-DQ) method proposed by (Shu, Ding, and Yeo (2003)) is a natural mesh- freeapproach forderivativeapproximation,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, thismesh-free methodwasextendedtosim- ulate fluid flow problems with curved boundary in three-dimensional (3D) space. The main con- cern of this work is to numerically study the per- formance of the 3D local MQ-DQ method and demonstrate its capability and flexibility for sim- ulation 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 com- pared well with available data in the literature. The numerical solution shows that the local MQ- DQ method can be applied to solve incompress- ible viscous flow problems with curved boundary in 3D space effectively. Keyword: Local MQ-DQ method; Error esti- mate; Flow past a sphere
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