A new boundary treatment method in smoothed particle hydrodynamics

As the smoothed particle hydrodynamics (SPH) is a truly Lagrangian meshfree method, the implementation of solid boundary condition has been one of the key problems that hinder SPH from applying to lots of engineering problems. In order to treat the boundary conditions efficiently, based on the boundary-fluid interaction principles, a new boundary treatment method is proposed. In this method, the solid boundary is represented implicitly by several layers of dummy particles along the boundary line. During the simulation, the dummy particles are treated as an extension of the fluid phase. The densities of dummy particles are kept constant, and the pressures and velocities are interpolated from the nearby fluid particles at each time step. Dummy particles can be involved in the calculation of the continuity equation conditionally and exert influences on the density/ pressure field of the fluid phase. Then, for the fluid particles that approach the solid boundary, local pressure gradients are used to represent the dummy-fluid particle pair's interaction strength and act as the boundary force term implicitly, which is tuned to be repulsive only and normal to the boundary. Thus, large pressure gradients mean strong boundary-fluid interaction strength, and the boundary force from the dummy particles should also be large enough to prevent the fluid particles from penetrating the solid boundary; and on the contrary, small pressure gradients mean weak boundary-fluid interaction strength and the boundary force becomes soft and little disturbs the flow field. Results of numerical tests demonstrate that, compared with the existing boundary treatment methods, the new method is in better accordance with the physical principles of the fluid-boundary interaction, and is able to treat arbitrary solid boundaries with limited modeling and computational costs. With the help of this new boundary treatment method, the stable flow field, well-ordered particle distribution, smooth velocity and pressure fields could be obtained. Theoretically, this new boundary treatment method could be directly used in three-dimensional multi-phase problems. Further tests are planned to be carried out; meanwhile, expanding the new boundary treatment method to rigid-fluid interaction problems is also a work in the future.