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Reduced order models for Lagrangian hydrodynamics

As a mathematical model of high-speed flow and shock wave propagation in a complex multimaterial setting, Lagrangian hydrodynamics is characterized by moving meshes, advection-dominated solutions, and moving shock fronts with sharp gradients. These challenges hinder the existing projection-based mod...

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Bibliographic Details
Published in:Computer methods in applied mechanics and engineering 2022-01, Vol.388 (C), p.114259, Article 114259
Main Authors: Copeland, Dylan Matthew, Cheung, Siu Wun, Huynh, Kevin, Choi, Youngsoo
Format: Article
Language:English
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Summary:As a mathematical model of high-speed flow and shock wave propagation in a complex multimaterial setting, Lagrangian hydrodynamics is characterized by moving meshes, advection-dominated solutions, and moving shock fronts with sharp gradients. These challenges hinder the existing projection-based model reduction schemes from being practical. We develop several variations of projection-based reduced order model techniques for Lagrangian hydrodynamics by introducing three different reduced bases for position, velocity, and energy fields. A time-windowing approach is also developed to address the challenge imposed by the advection-dominated solutions. Lagrangian hydrodynamics is formulated as a nonlinear problem, which requires a proper hyper-reduction technique. Therefore, we apply the over-sampling DEIM and SNS approaches to reduce the complexity due to the nonlinear terms. Finally, we also present both a posteriori and a priori error bounds associated with our reduced order model. We compare the performance of the spatial and time-windowing reduced order modeling approaches in terms of accuracy and speed-up with respect to the corresponding full order model for several numerical examples, namely Sedov blast, Gresho vortices, Taylor–Green vortices, and triple-point problems. •We present reduced order models for Lagrangian hydrodynamics in parametric setting.•We derive efficient hyperrduction techniques for the compressible Euler equations.•We introduce time windowing approaches for temporally local dimension reduction.•We derive several error bounds for the reduced order model.•We present benchmark numerical experiments of compressible Euler equations.
ISSN:0045-7825
1879-2138
DOI:10.1016/j.cma.2021.114259