A Simplified SPH Method for Simulation of Free Surface Flows

In this study, SPH formulations are simplified based on straightforward mathematical operations for simulation of free surface flows. Satisfaction of boundary conditions, especially Neumann boundary conditions, is of great importance in accuracy of numerical methods. Employing dummy particles which are placed outside of wall boundaries is one of the simplest methods for imposing Neumann boundary conditions in which pressure of a dummy particle is set to that of a wall particle in the normal direction of the wall boundaries. In fact, dummy particles prevent fluid particles from penetration walls by imposing a repulsive pressure force. In spite of the simplicity of the method, initial placement of several lines of dummy particles can be difficult, especially for non-geometric computational domains. In this research, two different strategies are proposed and employed in which the wall conditions are modeled without the need of dummy particles. In the first strategy, contribution of dummy particles is indirectly included in the numerical computations based on their priori known positions. In the second and main strategy, dummy particles are entirely excluded from the computations and the wall conditions can be modeled only with the wall particles. The efficiency and accuracy of both strategies in modeling of the wall conditions are tested for simulation of dam-break flow using a well-known spline kernel function. It is found that water penetration across the walls is occurred for a certain range of radius of support domain, especially when the second strategy is employed. A new kernel function with steeper shape in comparison with the spline function is introduced here to prevent water penetration even for the second strategy. The efficiency of the proposed kernel function is tested by two free surface problems of dam break and Scott Russell wave generator.