Meshless Methods for 2D and 3D Incompressible Viscous Flows
Date Issued
2004
Date
2004
Author(s)
Jan, Shu-Jing
DOI
en-US
Abstract
The development of robust and efficient numerical algorithms for both steady-state and transient simulations of the Stokes equations and Navier-Stokes equations for two-dimensional and three-dimensional incompressible viscous flow is an active research field. A meshless method based on the multiquadrics (MQ) method has been developed to solve the 2D and 3D Stokes flows and Navier-Stokes equations in velocity-vorticity formulation. Numerical results are also reported using the method of fundamental solutions (MFS) in order to compare its performance with the MQ method. The method of fundamental solutions (MFS) based on the Stokeslet is successfully implemented for the numerical solution of Stokes flow problems. The MFS does not require a discretized interior domain and boundary integration to obtain the solutions for the flow variables. We implemented the MQ method to solve the Stokes equations and Navier-Stokes equations for two and three-dimensional flow problems. The method employed a coupled numerical solution algorithm by combining the boundary equations along with the governing equations to form a single global matrix for all the field variables. The computation of the velocity and the vorticity variables are completed by satisfying the continuity equation for the velocity field and the solenoidal constraint for the vorticity field. The multiquadrics method is found to be an efficient scheme for low Reynolds number flows, which has been demonstrated in this study. Two-dimensional and three-dimensional flow solutions for Stokes equations in a circular cavity, square cavity and cubic cavity are established and compared with available benchmark solutions by using both the MFS and MQ algorithms.
Subjects
MFS
納維爾史托克方程式
圓形穴室流
方形穴室流
無網格法
MQ
三維不可壓縮黏性流場
速度-渦度法
velocity-vorticity formulation
Stokes flows
meshless methods
incompressible Navier-Stokes equations
multiquadrics method
method of fundamental solutions
Type
thesis
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