Smoothed particle hydrodynamics continuous boundary force method for Navier–Stokes equations subject to a Robin boundary condition

A Robin boundary condition for the Navier–Stokes equations is used to model slip conditions at the fluid-solid boundaries. A novel continuous boundary force (CBF) method is proposed for solving the Navier–Stokes equations subject to the Robin boundary condition. In the CBF method, the Robin boundary condition is replaced by the homogeneous Neumann boundary condition and a volumetric force term added to the momentum conservation equation. ed particle hydrodynamics (SPH) method is used to solve the resulting Navier–Stokes equations. We present solutions for two- and three-dimensional flows subject to various forms of the Robin boundary condition in domains bounded by flat and curved boundaries. The numerical accuracy and convergence are examined through comparison of the SPH–CBF results with the solutions of finite difference or finite-element method. Considering the no-slip boundary condition as a special case of the slip boundary condition, we demonstrate that the SPH–CBF method accurately describes both the no-slip and slip conditions.