An adaptive support domain for the in-compressible fluid flow based on the localized radial basis function collocation method

In this paper, an adaptive support domain scheme is proposed to the in-compressible fluid flow based on the localized radial basis function collocation method (LRBFCM). The idea of the adaptive support domain avoids complex mathematical derivations of the finite difference method (FDM). Unlike other upwind schemes in the LRBFCM, the support domain uses the sampling nodes similar to different finite difference schemes, and the improved LRBFCM is further applied to the in-compressible fluid flows. Considering the Kronecker tensor product and Cholesky decomposition techniques, the improved LRBFCM can be easily used to the lid-driven problems with Reynolds numbers up to 100,000 by a simple mathematical derivation. The proposed LRBFCM has an adaptive support domain similar to the finite difference schemes with much less CPU time costs.