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

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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.

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Acknowledgements

The computing for this project was performed at the OSU High Performance Computing Center at Oklahoma State University.

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  1. Department of Mechanical and Aerospace Engineering, Oklahoma State University, Stillwater, OK, 74078, USA

    Mansoor Ahmed & Omer San

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  1. Mansoor Ahmed
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  2. Omer San
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Correspondence to Omer San.

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Communicated by Paul Cizmas.

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Ahmed, M., San, O. Stabilized principal interval decomposition method for model reduction of nonlinear convective systems with moving shocks. Comp. Appl. Math. 37, 6870–6902 (2018). https://doi.org/10.1007/s40314-018-0718-z

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  • DOI: https://doi.org/10.1007/s40314-018-0718-z

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