面向激波主导问题的自适应模型降阶方法
Self-Adaptive Model-Order Reduction for Shock-Dominated Problems
AI总结：
本研究提出一种自适应模型降阶框架，可根据解的演化特性动态选择自适应或静态ROM，兼顾计算效率与精度，在旋转爆震发动机建模中验证了其有效性。
摘要：
基于投影的模型降阶（MOR）通过构建保留全阶模型（FOM）大部分精度、同时大幅降低计算成本的降阶模型（ROM），为加速昂贵的全阶模型提供了有前景的方法。然而，遵循离线/在线训练策略的传统静态ROM，在处理激波等具有强演化物理特性的对流主导问题时，预测能力有限。自适应ROM作为有前景的替代方案，通过在线模拟过程中动态更新低维子空间以跟踪局部演化的系统动力学，从而即使对于激波主导的流动也能实现准确预测。但这种在线自适应会引入额外计算开销，频繁的基和采样点更新会大幅削弱其相对于静态ROM的计算优势。为协调这种权衡，本研究提出一种自适应MOR框架，在在线模型执行期间根据解的演化特性动态构建并部署最合适的ROM形式（自适应或静态），以在保持局部物理高建模精度的同时实现最优计算效率。该框架旨在利用自适应和静态ROM方法的优势，在减少对大量离线训练依赖的同时，实现最优计算效率和预测精度。该框架针对旋转爆震发动机（RDE）进行开发和评估，RDE提供了具有强对流主导、瞬态和多尺度反应流动动力学的挑战性测试环境。
英文摘要：
Projection-based model-order reduction (MOR) offers a promising approach for accelerating expensive full-order model (FOM) by constructing reduced-order models (ROMs) that retain the majority of FOM accuracy while significantly reducing the computational cost. However, conventional static ROMs, often following offline/online training strategy, can exhibit limited predictive capability for convection-dominated problems featuring strongly evolving physics such as shocks. Adaptive ROMs emerge as a promising alternative and address such limitation by dynamically updating the low-dimensional subspace during online simulation to track locally evolving system dynamics, thereby enabling accurate predictions even for shock-dominated flows. However, such online adaptation introduces additional computational overhead, and frequent basis and sampling-point updates can substantially reduce their computational advantage relative to their static counterpart. To reconcile this tradeoff, the current work introduces a self-adaptive MOR framework that dynamically constructs and deploys the most appropriate ROM formulation (either adaptive or static) on the fly according to the evolving characteristics of the solution. to achieve optimal computational efficiency while maintaining high modeling accuracy of the local physics during the online model execution. In this regard, the proposed framework seeks to exploit the advantages of both adaptive- and static-ROM approaches to achieve an optimal computational efficiency and predictive accuracy while reducing reliance on extensive offline training. The framework is developed and evaluated for modeling rotating detonation engines (RDEs), which provide a challenging test environment involving strongly convection-dominated, transient, and multiscale reacting-flow dynamics.
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