Matrix Product State for Computational Turbulent Scalar Mixing and Reaction
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The High-fidelity prediction of turbulent flows remains one of the most complex unsolved issues in classical computational physics. The simulation complexity escalates even further in reacting flows, due to exothermicity and turbulence-chemistry interaction. Direct numerical simulation (DNS), which fully accounts for the relevant range of temporal and spatial physical scales, is unfeasible for such systems. New paradigms of computational fluid dynamics are needed. In this work, a quantum-inspired approach based on tensor networks (TNs) is developed as such a paradigm. Originally developed for modeling of many-body quantum systems, TNs offer a structured approach to approximate high-dimensional fields using collections of low-rank tensors. Here, the matrix product state (MPS) is employed as a new framework with twofold purposes. First, the MPS is used to time evolve two-dimensional shear flow under non-reacting and nonpremixed chemically reacting conditions. Total reductions of 30\% in memory are demonstrated, accompanied by excellent agreement with DNS\@. Second, the MPS is used to construct truncated representations of three-dimensional isotropic turbulent flow data. The hydrodynamic field of an incompressible three-dimensional flow, as well as the field of a conserved Fickian scalar in a similar flow, are considered for MPS-based truncation. The velocity and scalar field reconstructions reach 99.8\% fidelity using only 5\% and 15\% of DNS memory, respectively. These results demonstrate the effectiveness of the MPS as a new effective framework in computational fluid dynamics, as well as a scalable reduced-order modeling technique for complex turbulent datasets.
