
Incremental Reduced-Order Modeling of Smoothed Particle Hydrodynamics
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The contribution describes the development and application of an incremental Singular Value Decomposition (SVD) strategy for compressing time-dependent particle simulation results. The approach is based on an algorithm originally developed for grid-based Finite-Volume simulations [1]. The presentation will explain how this technique can be further developed to process highly irregular data/snap-shot matrices generated by particle simulation methods [2]. Such unsteady particle simulations usually consist of several 10-100 million spatiotemporal entries, making standard procedures quickly unfeasible. Parallelized incremental updates of the SVD with the new, time-evolving data are one option to address the related challenges and can be helpful for processing and reusing such large amounts of data. In Smoothed-Particle Hydrodynamics (SPH) simulations, data matrix irregularity arises from the advection, injection, and deletion of particles during the simulation. Therefore, the particles lack data before their injection or after their deletion, which must be imputed. The performance of different imputation strategies for dealing with these temporarily inactive particles will be outlined. In addition, information loss, computational effort and storage requirements are explained, and corresponding solution techniques are investigated. These include the development of a heuristic adaptive rank truncation criterion, and a suggestion for sequencing the data history into temporal windows. To validate the method, the latter is embedded in a parallel, industrialized SPH software [3] and applied to classical dam break and impinging jet flows as well as a 3D rotating Pelton Runner. For a prescribed accuracy, memory requirements are reduced by about 90%, while the computational cost is only increased by about 10%. With regard to the final application of a water turbine, the temporal evolution of the force and torque values for the compressed and simulated data is in excellent agreement.