Stabilized principal interval decomposition method for model reduction of nonlinear convective systems with moving shocks

Abstract

An efficient and reliable model order reduction of nonlinear systems poses a challenge for nonstationary problems with convective, non-periodic, and non-equilibrium dynamics. To that end, we put forth a localized basis selection strategy based on the proper orthogonal decomposition (POD) and principal interval decomposition (PID) to construct a stable reduced-order modeling framework to capture the unsteady dynamics of nonlinear systems effectively. The implementation of an eddy viscosity (EV) based closure model in POD–PID approach yields the proposed POD–PID–EV projection-based reduced-order modeling approach for nonlinear partial differential equations. Solving the nonlinear Burgers’ equation with various spatio-temporal dynamical complexities, it is shown that the present approach yields significant improvements in accuracy over the standard POD–Galerkin model with a negligibly small computational overhead. Furthermore, we show that strong moving discontinuities can be effectively captured in the low-dimensional space with the proposed approach.