Reduced order modeling of time-dependent incompressible Navier-Stokes equation with variable density based on a local radial basis functions-finite difference (LRBF-FD) technique and the POD/DEIM method

The main propose of this investigation is to introduce a rapid and impressive numerical procedure to simulate the time dependent incompressible Navier-Stokes equation with variable density. The developed formulation is constructed by using the meshfree RBF-FD technique. Also, to improve the numerical results, an extra diffusion term has been added to the density equation with a small coefficient. On the other hand, a reduced order technique e.g. proper orthogonal decomposition (POD) has been employed to get a fast numerical method and to decrease the elapsed CPU time. On the other hand, since the considered problem is fully nonlinear, thus in the reduced order model based on the POD idea, there are some nonlinear terms that they take more computational time. Hence, we employ the discrete empirical interpolation method (DEIM) to overcome the nonlinear terms. Four test problems have been proposed to show the ability of the numerical simulations. (C) 2020 Elsevier B.V. All rights reserved.