Meshless methods applied to computational fluid dynamics (CFD) are relatively new areas of research. The local RBF-DQ is a natural meshless method, which combines derivative approximation by differential quadrature (DQ) method and functional approximation by radial basis function (RBF), so that the derivatives of dependent variables can be directly approximated on a scattered set of nodes. In this paper, we mainly concentrate on the multiquadric RBFs, since they have exponential convergence. The ability of the method of RBF-DQ to deal with the problems of fluid mechanics is demonstrated in this paper by applications to different types of flow problems. The comparison of this method based on accuracy and the speed of the method, with other established schemes like FVM, FDM, etc., is in process and being carried out presently. Results obtained are compared with analytical solutions and published data. It is found that the present mesh-free results agree very well with available data in the literature.
|Number of pages||55|
|Journal||International Journal of Numerical Methods and Applications|
|Publication status||Published - 2012|