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:本文提出了一个战略, 用于为时间变化、 空间 3D 离散数据集构建递增 Singal 值分解( SVD) 的递增 Singal 值分解( SVD) 。 提供了一个用于减少和部署快照数据的低存储存取程序。 考虑的例子是指从不稳定流模拟中提取的计算液流动态( CFD), 该模拟利用域分解战略进行空间平行计算。 框架针对用于实际应用的艺术 PDE 解析( SVD) 状态。 虽然该方法适用于技术流, 但也适用于Computurational 科学与工程( CSEE) 伞下的类似应用。 为此, 我们引入了一组矩阵矩阵, 允许聚合多时间步骤和 SVD 更新, 并大大提高计算效率。 递增 SVD 战略最初通过模拟圆柱形圆柱形 2D 的单级流流流。 随后的研究表明, 2D 淹没的流流流流流流流流流流流流流战略可以持续到 。 以当地和全球 流流流流流流流流值 的 Slev 递递递递递递递递递递减 递减 值 值 递递递增 的OO. 0L 的递增 的递增过程的精确度 。