We present a new methodology for decomposing flows with multiple transports that further extends the shifted proper orthogonal decomposition (sPOD). The sPOD tries to approximate transport-dominated flows by a sum of co-moving data fields. The proposed methods stem from sPOD but optimize the co-moving fields directly and penalize their nuclear norm to promote low rank of the individual data in the decomposition. Furthermore, we add a robustness term to the decomposition that can deal with interpolation error and data noises. Leveraging tools from convex optimization, we derive three proximal algorithms to solve the decomposition problem. We report a numerical comparison with existing methods against synthetic data benchmarks and then show the separation ability of our methods on 1D and 2D incompressible and reactive flows. The resulting methodology is the basis of a new analysis paradigm that results in the same interpretability as the POD for the individual co-moving fields.

翻译：本文提出了一种处理具有多重输运特征的流动分解的新方法，进一步拓展了移位本征正交分解（sPOD）框架。sPOD通过将输运主导的流动近似为多个共移动数据场的叠加。本文方法源于sPOD，但直接优化共移动场，并通过惩罚其核范数来促进分解中各数据场的低秩性。此外，我们在分解中引入鲁棒项以处理插值误差和数据噪声。借助凸优化工具，我们推导了三种近端算法来求解该分解问题。通过合成数据基准与现有方法的数值对比，我们展示了该方法在一维和二维不可压缩及反应流中的分离能力。最终方法论构成了新的分析范式基础，使各共移动数据场具备与传统POD相同的可解释性。