An investigation into the nonlinear effects in the roll motion of 2-D bodies by SPH method

Nonlinear effects in the roll motion of a 2-D body in the free surface are investigated by utilizing the Smoothed Particle Hydrodynamics (SPH) method. The continuity and Navier-Stokes equations are solved by employing the Weakly Compressible SPH (WCSPH) approach and our in-house code, which relies on the accumulated development process through the authors' previous works including the fluid-solid coupling modeling by viscous penalty technique, (Tofighi et al. (2015)), and a hybrid Velocity-Variance Free Surface (VFS) and Artificial Particle Displacement (APD) algorithm (Ozbulut et al., 2014, 2018, 2020; Kolukisa et al., 2020). In this work, the GPU parallelization of the code is performed, to mitigate the computational burdens of the relatively high number of particles due to the long wavelengths generated by the roll motion of the cylinder. Presently, an alternative and exact approach in reducing the equation of roll motion with quadratic damping term is introduced. In parallel to this approach, a quadratic regression equation approximating the hydrodynamic roll moment is also employed. Aside from hydrodynamic coefficients, with linear and quadratic damping coefficients, vortex flow characteristics are also presented, qualitatively and quantitatively. It is understood from the results that, with the present capability, the WCSPH approach introduced is able to disclose nonlinearities inherently exist in the roll motion of oscillatory bodies in the free surface.