A Hybrid Solver Based on Efficient BEM-Potential and LBM-NS Models: Recent LBM Developments and Applications to Naval Hydrodynamics

O'Reilly, C. M. (University of Rhode Island, Navatek Ltd.) | Grilli, S. T. (University of Rhode Island) | Harris, J. C. (Université Paris-Est) | Mivehchi, A. (University of Rhode Island) | Janssen, C. F. (Hamburg University of Technology (TUHH)) | Dahl, J. M. (University of Rhode Island)



We report on recent progress and validation of a 3D hybrid model for naval hydrodynamics problems based on a perturbation method, in which both velocity and pressure are expressed as the sum of an inviscid flow with a viscous perturbation. The far- to near-field inviscid flows can be solved with a Boundary Element Method (BEM), based on fully nonlinear potential flow theory, and the near-field perturbation flow is solved with a NS model based on a Lattice Boltzmann Method (LBM) with a Large Eddy Simulation (LES) of the turbulence. We summarize the hybrid model formulation and latest developments regarding the LES, and particularly a new wall model for the viscous/turbulent sub-layer near solid boundaries, that is generalized for an arbitrary geometry. The latter are validated by simulating turbulent flows over a flat plate for Re ∈ [3.7 × 104; 1.2 × 106], for which the friction coefficient computed on the plate agrees well with experiments. We then simulate the flow past a NACA0012 foil using the hybrid LBM-LES with the wall model, for Re = 1 × 106, and show a good agreement of lift and drag forces with experiments. Results obtained with the hybrid LBM model are either nearly identical or improved relative to those of the standard LBM, but for a smaller computational domain, demonstrating the benefits of the hybrid approach.


The simulation of large ship motions and resistance in steep waves is typically performed using linear or (more rarely) nonlinear potential flow solvers, usually based on a higher-order Boundary Element Method (BEM), with semi-empirical corrections introduced to account for viscous/turbulent effects. However in some cases, viscous/turbulent flows near the ship's hull, and breaking waves and wakes must be accurately modeled to capture the salient physics. Navier-Stokes (NS) solvers can and have been used to model such flows, but they are computationally expensive and often too numerically dissipative to model wave propagation over long distances.