Incremental Reduced-Order Modeling of Smoothed Particle Hydrodynamics
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The contribution describes a Singular Value Decomposition (SVD) based approach to reduce the dimensionality of data obtained from a Smoothed Particle Hydrodynamics (SPH) simulation. Since complete datasets obtained from unsteady simulations usually consist of several 10-100 million spatial-temporal entries, standard procedures become quickly unfeasible. Incremental updates of an SVD with the new, temporally evolving data can be a way to address this issue. In case of particle related SPH data, the data is not only advected with the particles in the domain but may also be injected or deleted, e.g. if the particles leave the domain or violate physical constraints. As a result, this may lead to highly irregular state vectors of different length, and a data matrix where particle related entries may lack data before their generation or after their deletion. We present an order reducing approach to account for particle displacement, injection, deletion. To validate the method for the efficient reconstruction of SPH based simulation results, classical dam break and impinging jet flows are studied. The presentation also scrutinizes the associated computational overheads, and the fidelity of the reconstruction.