Nonlinear model order reduction of Burgers' Equation using proper orthogonal decomposition

In this paper, we examine a model order reduction approach for dynamic systems governed by Burgers' equation with Neumann boundary conditions. The proper orthogonal decomposition (POD) method is employed here that provides a reliable and accurate modeling approach, while the temporal discretization of the continuous error function leads to a more accurate estimation of the defined cost function. We will investigate the accuracy of the reduced-order model compared to the finite element (FE) model by choosing an adequate number of basis functions for the approximating subspace. The derived lumped-parameter model for Burgers' equation is then described by a nonlinear state-space model. We finally demonstrate the accuracy of the reduced-order model through a numerical example, where we show that a 7-dimensional POD can accurately estimate the system output.

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