The paper presents a strategy to construct an incremental Singular Value Decomposition (SVD) for time-evolving, spatially 3D discrete data sets. A low memory access procedure for reducing and deploying the snapshot data is presented. Considered examples refer to Computational Fluid Dynamic (CFD) results extracted from unsteady flow simulations, which are computed spatially parallel using domain decomposition strategies. The framework addresses state of the art PDE-solvers dedicated to practical applications. Although the approach is applied to technical flows, it is applicable in similar applications under the umbrella of Computational Science and Engineering (CSE). To this end, we introduce a bunch matrix that allows the aggregation of multiple time steps and SVD updates, and significantly increases the computational efficiency. The incremental SVD strategy is initially verified and validated by simulating the 2D laminar single-phase flow around a circular cylinder. Subsequent studies analyze the proposed strategy for a 2D submerged hydrofoil located in turbulent two-phase flows. Attention is directed to the accuracy of the SVD-based reconstruction based on local and global flow quantities, their physical realizability, the independence of the domain partitioning, and related implementation aspects. Moreover, the influence of lower and (adaptive) upper construction rank thresholds on both the effort and the accuracy are assessed. The incremental SVD process is applied to analyze and compress the predicted flow field around a Kriso container ship in harmonic head waves at Fn = 0.26 and ReL = 1.4E+07. With a numerical overhead of O(10%), the snapshot matrix of size O(R10E+08 x 10E+04) computed on approximately 3000 processors can be incrementally compressed by O(95%). The storage reduction is accompanied by errors in integral force and local wave elevation quantities of O(1E-02%).

翻译：本文提出了一种针对随时间演化的三维空间离散数据集的增量奇异值分解（SVD）构建策略。文中介绍了一种低内存访问的降阶与快照数据部署规程。所考虑的实例涉及从非定常流动模拟中提取的计算流体动力学（CFD）结果，这些模拟采用区域分解策略进行空间并行计算。该框架面向专用于实际应用的现代偏微分方程求解器。尽管该方法应用于技术流动，但同样适用于计算科学与工程（CSE）领域内的类似应用。为此，我们引入了一个批量矩阵，允许聚合多个时间步并更新SVD，从而显著提高计算效率。该增量SVD策略首先通过模拟二维层流单相流绕圆柱流动得到验证与确认。后续研究分析了该策略在湍流两相流中二维浸没水翼上的应用。重点关注基于局部与全局流动量的SVD重构精度、其物理可实现性、区域分解的独立性及相关实现问题。此外，评估了下限与（自适应）上限构建秩阈值对计算开销与精度的影响。将增量SVD过程应用于分析并压缩Kriso集装箱船在谐波顶浪条件下（弗劳德数Fn=0.26，雷诺数ReL=1.4E+07）的预测流场。在数值开销约为10%的情况下，由约3000个处理器计算生成的规模约为O(1E+08 x 1E+04)的快照矩阵可被增量压缩约95%。存储缩减伴随着积分力与局部波高量的误差约为O(1E-02%)。