Non-intrusive reduced-order modelling of the Navier-Stokes equations based on RBF interpolation

We present a new non-intrusive model reduction method for the Navier-Stokes equations. The method replaces the traditional approach of projecting the equations onto the reduced space with a radial basis function (RBF) multi-dimensional interpolation. The main point of this method is to construct a number of multi-dimensional interpolation functions using the RBF scatter multi-dimensional interpolation method. The interpolation functions are used to calculate POD coefficients at each time step from POD coefficients at earlier time steps. The advantage of this method is that it does not require modifications to the source code (which would otherwise be very cumbersome), as it is independent of the governing equations of the system. Another advantage of this method is that it avoids the stability problem of POD/Galerkin. The novelty of this work lies in the application of RBF interpolation and POD to construct the reduced-order model for the Navier-Stokes equations. Another novelty is the verification and validation of numerical examples (a lock exchange problem and a flow past a cylinder problem) using unstructured adaptive finite element ocean model. The results obtained show that CPU times are reduced by several orders of magnitude whilst the accuracy is maintained in comparison with the corresponding high-fidelity models. Copyright (C) 2015 John Wiley & Sons, Ltd.