A Non-Intrusive Reduced-Order Model Developed for Parameterized Time-Dependent Problems

For parameterized time-dependent problems, we propose to adopt two-level proper decomposition to extract temporal and spatial basis functions and radial basis function(RBF) model to be used to approximate the undetermined coefficients, thus forming a non-intrusive reduced order method(ROM), of which the approximation process doesn't rely on the governing equation after reduced basis obtained. In order to reduce the dependence of RBF on empirical parameters, a new RBF which exerts QR decomposition and other mathematical approaches on the standard RBF is used in our proposed ROM. When approximating one-dimensional Burgers equation and a driven cavity problem governed by incompressible Navier-Stokes equations, results show that the non-intrusive ROM predicts the unsteady flow field fast and accurately at any point in the parameter domain.