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arXiv · 2104.11404

Reduced order models for Lagrangian hydrodynamics

Dylan Matthew Copeland·Siu Wun Cheung·Kevin Huynh·Youngsoo Choi
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Abstract

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.

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Dylan Matthew Copeland, Siu Wun Cheung, Kevin Huynh, Youngsoo Choi. 2021-04-23. Reduced order models for Lagrangian hydrodynamics. https://doi.org/10.1016/j.cma.2021.114259

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