Quantum-Inspired tensor-network fractional-step method for incompressible flow in curvilinear coordinates

Journal
Computer physics communications  
Citation
Computer Physics Communications (in Press): (2026)
Publisher DOI
10.1016/j.cpc.2026.110169
Publisher
Elsevier BV
We introduce an algorithmic framework based on tensor networks for computing fluid flows around immersed objects in curvilinear coordinates. We show that the tensor network simulations can be carried out solely using highly compressed tensor representations of the flow fields and the differential operators and discuss the numerical implementation of the tensor operations required for computing fluid flows in detail. The applicability of our method is demonstrated by applying it to the paradigm example of steady and transient flows around stationary and rotating cylinders. We find excellent quantitative agreement in comparison to finite difference simulations for Strouhal numbers, forces and velocity fields. The properties of our approach are discussed in terms of reduced order models. We estimate the memory saving and potential runtime advantages in comparison to standard finite difference simulations. We find accurate results with errors of less than 0.3% for flow-field compressions by a factor of up to 20 and differential operators compressed by factors of up to 1000 compared to sparse matrix representations. We provide strong numerical evidence that the runtime scaling advantages of the tensor network approach with system size will provide substantial resource savings when simulating larger systems. Finally, we note that, like other tensor network-based fluid flow simulations, our algorithmic framework is directly portable to a quantum computer leading to further scaling advantages.
Subjects
Quantum Computational Fluid Dynamics
Quantics Tensor Trains
Quantum-Inspired Flow Solver
Curvilinear Coordinates
Reduced order modeling
Navier-Stokes Flow
DDC Class
530: Physics
623.8: Naval Architecture; Shipbuilding
004: Computer Sciences