Tensor networks (TN) provide a powerful framework for compressing large datasets to reduced computational complexity while maintaining fundamental details.As computational fluid dynamics tend towards ever-increasing resolutions[1],these techniques offer a promising alternative for reducing computational effort.In this regard,we present a computational environment using one-dimensional TN,viz.,tensor-train (TT) methods,to simulate an incompressible viscous fluid.Our contribution presents a fractional-step Navier-Stokes algorithm in TT format.To this end,the complete time-marching pressure-correction algorithm of Armfield & Street[1]is recompiled into tensor network operations.Additionally,pressure-velocity coupling on collocated grids in the TT realm is reinforced using the Rhie-Chow interpolation scheme[1],while the immersed boundary method[2]enables representation of complex geometries through binary masks.The latter is of particular importance,in contrast to curvilinear coordinates employed in previous work[3],for generalizing the study of internal flows.All problem states—velocity fields,pressure,and geometry masks—remain in TT representation throughout the computation.We demonstrate the framework's capabilities,by way of example,for a laminar flow through a two-dimensional S-bend channel,evaluating complexity and accuracy against conventional finite-difference implementations.Furthermore,compression characteristics and computational performance are analyzed regarding the accuracy of the solution.To this end,our contribution extends quantum-inspired tensor network methodologies for fluid dynamics[3]and provides a foundation for tensor-programmable solvers[4,5],establishing practical pathways towards quantum-computational approaches for industrial flow simulations. REFERENCES [1]J.H.Ferziger et al.,"Computational methods for fluid dynamics," vol.586.Springer,2002. [2]C.S.Peskin,"Flow patterns around heart valves:a numerical method,"J.Comput.Phys.,vol.10,no.2,pp.252–271,1972. [3]N.-L.van Hülst et al.,"Quantum-inspired tensor-network fractional-step method for incompressible flow in curvilinear coordinates,"2025.(preprint:arXiv:2507.05222). [4]P.Siegl et al.,"Tensor-programmable quantum circuits for solving differential equations,"Phys.Rev.Res.,vol.8,p.013052,2026. [5]P.Over et al.,"Boundary treatment for variational quantum simulations of partial differential equations on quantum computers,"Computers & Fluids,vol.288,p.106508,2025.