利用隐式特征跟踪和经验正交加速求解对流主导偏微分方程

IF 1.7 4区 工程技术 Q3 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS
Marzieh Alireza Mirhoseini, Matthew J. Zahr
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引用次数: 1

摘要

本研究介绍了一种基于经验正交的超还原程序和贪婪训练算法,以有效降低在有限训练条件下求解对流主导问题的计算成本。所提出的方法规避了应用于对流主导问题的线性模型还原技术的 n$ n$ 宽度缓慢衰减的限制,它使用了一个非线性近似流形,该流形是通过将低维仿射空间与底层域的双射组成而系统定义的。减阶模型被定义为非线性流形上残差最小化问题的解。通过使用经验正交来逼近最优系统,从而获得了一种在线高效方法,该方法可以通过与网格无关的操作来求解。利用贪婪程序对参数域进行系统采样,从而训练出拟议的降阶模型。在两个以冲击为主的计算流体动力学基准上演示了所提方法的有效性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

Accelerated solutions of convection-dominated partial differential equations using implicit feature tracking and empirical quadrature

Accelerated solutions of convection-dominated partial differential equations using implicit feature tracking and empirical quadrature

This work introduces an empirical quadrature-based hyperreduction procedure and greedy training algorithm to effectively reduce the computational cost of solving convection-dominated problems with limited training. The proposed approach circumvents the slowly decaying n $$ n $$ -width limitation of linear model reduction techniques applied to convection-dominated problems by using a nonlinear approximation manifold systematically defined by composing a low-dimensional affine space with bijections of the underlying domain. The reduced-order model is defined as the solution of a residual minimization problem over the nonlinear manifold. An online-efficient method is obtained by using empirical quadrature to approximate the optimality system such that it can be solved with mesh-independent operations. The proposed reduced-order model is trained using a greedy procedure to systematically sample the parameter domain. The effectiveness of the proposed approach is demonstrated on two shock-dominated computational fluid dynamics benchmarks.

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来源期刊
International Journal for Numerical Methods in Fluids
International Journal for Numerical Methods in Fluids 物理-计算机:跨学科应用
CiteScore
3.70
自引率
5.60%
发文量
111
审稿时长
8 months
期刊介绍: The International Journal for Numerical Methods in Fluids publishes refereed papers describing significant developments in computational methods that are applicable to scientific and engineering problems in fluid mechanics, fluid dynamics, micro and bio fluidics, and fluid-structure interaction. Numerical methods for solving ancillary equations, such as transport and advection and diffusion, are also relevant. The Editors encourage contributions in the areas of multi-physics, multi-disciplinary and multi-scale problems involving fluid subsystems, verification and validation, uncertainty quantification, and model reduction. Numerical examples that illustrate the described methods or their accuracy are in general expected. Discussions of papers already in print are also considered. However, papers dealing strictly with applications of existing methods or dealing with areas of research that are not deemed to be cutting edge by the Editors will not be considered for review. The journal publishes full-length papers, which should normally be less than 25 journal pages in length. Two-part papers are discouraged unless considered necessary by the Editors.
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