2025/09/14 by Ye Ji, Monica Lăcătuş, Ji, Ye +3
Engineering · #Aerodynamics and Fluid Dynamics Research #Fluid Dynamics and Turbulent Flows #Lattice Boltzmann Simulation Studies #cs.NA #math.NA #physics.flu-dyn
paper · pdf · doi:10.48550/arxiv.2509.11427
openalex publication_date 2025/09/14 · openalex created_date 2025/10/12 · openalex updated_date 2026/07/28
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 = cs2 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(Ma2) 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.