# Perturbation LBM

The perturbation LBM branch of elbe is used in conjunction with an inviscid solver, such as a boundary element method (BEM), to simulate complex naval hydrodynamics problems such as ship resistance, seakeeping and maneuvering. These simulations are typically performed using a BEM alone, with semi empirical corrections introduced to account for viscous/turbulent effects; this yields medium-fidelity, but computationally efficient results. However, in some cases viscous/turbulent flows and wave breaking near the ship’s hull must be more accurately modeled. Navier-Stokes (NS) solvers, such as LBM and finite volume methods, can and have been used to model such flows, but they are often too computationally expensive to be used in engineering analyses. Elbe’s perturbation LBM approach combines the computationally efficient BEM with the high-fidelity of a NS solver by applying the LBM only to the near-field, where viscous/turbulent effects matter. In this hybrid decomposition approach, the LBM solution is forced by results of the BEM, applied to the entire domain, the latter capturing the large-scale and mainly inviscid solution of the radiated, diffracted, or incoming waves. This approach allows performing high-fidelity simulations of complex naval hydrodynamics problems that would typically require a large CPU cluster, on a desktop computer where the BEM problem is solved on CPU processors and the LBM on a standard GPGPU.

Recent research developments of the hybrid BEM-LBM approach have focused on extending the method to high Reynolds number applications. These include the development of a perturbation LBM multiple relaxation time collision operator and sub-grid scale turbulent closure schemes that use the large eddy simulation (LES) approach combined with a near wall turbulent boundary layer model. Further developments include using NURBS (B-splines) to describe the geometry of complex naval structures, with the help of meshing tools, and a hybrid volume of fluid (VOF) free surface capturing method that solves fully nonlinear free surface flow problems, by way of a mapping between the LBM and BEM free surface solutions.

Figure 1: Simulation of a Series 60 hull using the hybrid method on a reduced viscous domain. The free surface elevation is shown on the top surface and total inviscid solution is provided by a BEM solution.

Figure 2: Selected snapshots of a nonlinear wave, simulated with a potential flow solution, interacting with a solid cylinder. The wakes generated were calculated using the nonlinear hybrid VOF free surface solver in elbe.

Christopher O’Reilly [www]

Prof. Stéphan T. Grilli [www]

University of Rhode Island

- C.F. Janßen, S.T. Grilli and M. Krafczyk, "Modeling of Wave Breaking and Wave-Structure Interactions by Coupling of Fully Nonlinear Potential Flow and Lattice-Boltzmann Models", in: Proc. ISOPE 2010.
- A. Mivehchi, J.C. Harris,S.T. Grilli, J.M. Dahl, C.M.O’Reilly, K.Kuznetsov and C.F. Janßen, "A Hybrid Solver Based on Efficient BEM-potential and LBM-NS models: Recent BEM Developments and Applications to Naval Hydrodynamics", in: Proc. ISOPE 2017.
- C.M. O’Reilly, S.T. Grilli, J.C. Harris, A. Mivehchi, C.F. Janßen, J.M. Dahl, "A Hybrid Solver Based on Efficient BEM-potential and LBM-NS Models: Recent LBM Developments and Applications to Naval Hydrodynamics.", in: Proc. ISOPE 2017.