Solutions of 2D and 3D Stokes laws using multiquadrics method
In this paper, velocityvorticity formulation and the multiquadrics method (MQ) with iterative scheme are used to solve two (2D) and three-dimensional (3D) steady-state incompressible Stokes cavity flows. The method involves solving of Laplace type vorticity equations and Poisson type velocity equations. The solenoidal velocity and vorticity components are obtained by iterative procedures through coupling of velocity and vorticity fields. Both the Poisson type velocity equations and the Laplace type vorticity equations are solved using the MQ, which renders a meshless (or meshfree) solution. Here, the results of 2D Stokes flow problems in a typical square cavity and a circular cavity are presented and compared with other model results. Besides utilizing the MQ to solve the 3D Stokes cubic cavity flow problem, we are also obtaining promising results for the accuracy of the velocity and vorticity. The MQ model has been found to be very simple and powerful for analyzing the 2D and 3D internal Stokes flow problems.
multiquadrics method velocityvorticity formulation three-dimensional meshless stokes flow square cavity circular cavity cubic cavity iterative solution two-dimensional