The modification of boundary treatment in the incompressible sph for pressure calculation accuracy on the solid boundary

The Incompressible Smoothed Particle Hydrodynamic (ISPH) is one of the particle methods and commonly used to solve some complicated physical problems including free surface flow problems. The study regarding the boundary treatment has become an active research area in the mesh-free or particle method recently for measuring the accurate and robust pressure near the boundary. The penetrations of fluid particles may be happened if the adequate pressure boundary condition on the solid boundary cannot be satisfied. In this paper, a simple boundary treatment, which can be satisfied the non-homogenous Neumann boundary condition on the solid boundary and Dirichlet condition on the water surface, is proposed. The key point of our proposed treatment is that these boundary conditions are automatically satisfied by solving a modified pressure Poisson equation. Lastly, the effectiveness and accuracy of boundary treatment proposed are then authenticated with couples of numerical analysis and compared with the experimental tests.