An enhanced treatment of boundary conditions in implicit smoothed particle hydrodynamics

In this work, an enhanced treatment of the solid boundaries is proposed for smoothed particle hydrodynamics with implicit time integration scheme (Implicit SPH). Three types of virtual particles, i.e., boundary particles, image particles and mirror particles, are used to impose boundary conditions. Boundary particles are fixed on the solid boundary, and each boundary particle is associated with two fixed image particles inside the fluid domain and two fixed mirror particles outside the fluid domain. The image particles take the flow properties through fluid particles with moving least squares (MLS) interpolation and the properties of mirror particles can be obtained by the corresponding image particles. A repulsive force is also applied for boundary particles to prevent fluid particles from unphysical penetration through solid boundaries. The new boundary treatment method has been validated with five numerical examples. All the numerical results show that Implicit SPH with this new boundary-trearment method can obtain accurate results for non-Newtonian fluids as well as Newtonian fluids, and this method is suitable for complex solid boundaries and can be easily extended to 3D problems.