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Reduced order models for Lagrangian hydrodynamics
Computer Methods in Applied Mechanics and Engineering ( IF 7.2 ) Pub Date : 2021-11-10 , DOI: 10.1016/j.cma.2021.114259
Dylan Matthew Copeland 1 , Siu Wun Cheung 1 , Kevin Huynh 2 , Youngsoo Choi 1
Affiliation  

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.



中文翻译:

拉格朗日流体动力学的降阶模型

作为复杂多材料环境中高速流动和激波传播的数学模型,拉格朗日流体动力学的特点是移动网格、对流主导解和具有陡峭梯度的移动激波前沿。这些挑战阻碍了现有的基于投影的模型缩减方案的实用性。我们通过为位置、速度和能量场引入三种不同的简化基,为拉格朗日流体动力学开发了几种基于投影的降阶模型技术的变体。还开发了一种时间窗口方法来解决由对流主导的解决方案带来的挑战。拉格朗日流体动力学被表述为一个非线性问题,需要适当的超还原技术。所以,我们应用过采样 DEIM 和 SNS 方法来降低非线性项的复杂性。最后,我们还提出了与我们的降阶模型相关的后验和先验误差界限。我们比较了空间和时间窗口降阶建模方法在精度和加速方面的性能与几个数值示例的相应全阶模型的性能,即 Sedov 爆炸、Gresho 涡流、Taylor-Green 涡流和三重-点问题。

更新日期:2021-11-10
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