Introduction to statistical pattern recognition (2nd ed.)
Introduction to statistical pattern recognition (2nd ed.)
Nonlinear Model Reduction via Discrete Empirical Interpolation
SIAM Journal on Scientific Computing
A State Space Error Estimate for POD-DEIM Nonlinear Model Reduction
SIAM Journal on Numerical Analysis
Journal of Computational Physics
POD reduced-order unstructured mesh modeling applied to 2D and 3D fluid flow
Computers & Mathematics with Applications
POD/DEIM nonlinear model order reduction of an ADI implicit shallow water equations model
Journal of Computational Physics
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This article presents a new reduced order model based upon proper orthogonal decomposition (POD) for solving the Navier-Stokes equations. The novelty of the method lies in its treatment of the equation's non-linear operator, for which a new method is proposed that provides accurate simulations within an efficient framework. The method itself is a hybrid of two existing approaches, namely the quadratic expansion method and the Discrete Empirical Interpolation Method (DEIM), that have already been developed to treat non-linear operators within reduced order models. The method proposed applies the quadratic expansion to provide a first approximation of the non-linear operator, and DEIM is then used as a corrector to improve its representation. In addition to the treatment of the non-linear operator the POD model is stabilized using a Petrov-Galerkin method. This adds artificial dissipation to the solution of the reduced order model which is necessary to avoid spurious oscillations and unstable solutions. A demonstration of the capabilities of this new approach is provided by solving the incompressible Navier-Stokes equations for simulating a flow past a cylinder and gyre problems. Comparisons are made with other treatments of non-linear operators, and these show the new method to provide significant improvements in the solution's accuracy.