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arXiv · 2509.11427

IGA-LBM: Isogeometric lattice Boltzmann method

Ye Ji·Monica Lăcătuş·Matthias Möller
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Abstract

The lattice Boltzmann method (LBM) offers intrinsic parallelism and simple boundary treatment, but Cartesian lattices approximate curved boundaries by stair steps, causing spurious forces and boundary-layer errors. We present an isogeometric collocation lattice Boltzmann method (IGA-LBM) that solves the discrete-velocity BGK system in strong form on body-fitted B-spline and NURBS geometries. Distribution functions are collocated at Greville points, advection is evaluated with high-order operators on the exact spline mapping, and time integration uses a four-stage Runge-Kutta scheme. Exact geometric metrics preserve a uniform free stream to machine precision on curved grids while retaining formal accuracy. The analysis recovers the incompressible Navier-Stokes equations with viscosity nu = cs^2 tau and shows that the main isogeometric advantage is exact geometry rather than a new interior stencil. Centered collocation is stabilized by a high-order filter, a physical-node closure restores fourth-order accuracy near clustered walls, and stiff collision limits the explicit step to dt <= 2.785 tau, scaling as O(Re^-1). Tests confirm the predicted accuracy and the O(Ma^2) compressibility floor. Validation covers the Ghia lid-driven cavity, steady and unsteady flow past a circular cylinder, and a body-fitted NACA0012 airfoil. For the cylinder, recirculation length is within about 9 percent and the Strouhal number within about 2.5 percent of reference values; drag is 6-12 percent above consensus and decreases with refinement, with stable wakes up to Re = 1000. For NACA0012 at Re = 500 and 10 degrees incidence, surface pressure and skin friction agree with reference data within a few percent. The method provides a high-order, free-stream-preserving LBM for curved-boundary flows based on exact B-spline and NURBS geometry, with demonstrated accuracy, stability, and geometric fidelity.

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BibTeXRIS

Ye Ji, Monica Lăcătuş, Matthias Möller. 2026-07-19. IGA-LBM: Isogeometric lattice Boltzmann method. https://arxiv.org/abs/2509.11427

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