Abstract: In order to simulate the process of raindrops hitting branches and other irregular boundary,
research has been conducted on the force of the fluid particles on solid boundaries represented by the
grid. A kind of boundary force simulation method without particle sampling is proposed. This
approach exploits the Gauss quadrature rules to integrate the triangular patches of a mesh model and
correct the particle density on the solid-liquid boundary. In addition, several parameters, including
pressure and viscous forces on the solid-liquid boundary, are also calculated using an integral
method to ensure the continuity of the boundary force and avoid a splashing phenomenon at the
moment of particles’ beating the boundary. Meanwhile, this paper propounds an attractive force
model to control the movement of the boundary particles flowing down on the surface of an object.
The experimental results reveal that the approaches proposed in this paper can achieve more realistic
effects of phenomenon simulations, such as the raindrop spreading, retracting and flowing along the
boundary, etc.

Key words: smoothed particle hydrodynamics, gauss quadrature rules, boundary conditions, liquids