Simulation flows with multiple phases and components via the radial basis functions-finite difference (RBF-FD) procedure: Shan-Chen model

Abstract

The current paper describes a rapid and impressive numerical technique to simulate the flows with multiple phases and components based upon the Shan-Chen model. The Shan-Chen model is a generalization of the incompressible Navier-Stokes equation with the variable density. The local radial basis function-generated finite difference method or local RBF-FD approach has been developed to solve the considered model. Furthermore, to get acceptable results, an extra diffusion term has been added to the density equation with a small coefficient. A reduced order technique e.g. proper orthogonal decomposition (POD) idea has been utilized to achieve a fast numerical procedure and to decrease the elapsed CPU time. The proposed numerical experiments show the ability, efficiency and acceptable results of the presented numerical scheme.