An improved incompressible SPH with unified semi-analytical wall boundary conditions for free surface flow

An enhanced treatment of the free surface boundary in the incompressible smoothed particle hydrodynamics (ISPH) method using the unified semi-analytical wall (USAW) boundary is proposed in this work. The instability problem at the free surface caused by kernel truncation can be resolved by assuming some virtual particles around the surface. The pressure of the virtual particles is considered as zero to impose pressure boundary conditions on the free surface, while the pressure of free surface particles is set to be a tiny value to reduce particle accumulation. To further improve the stability, the non-penetration algorithm is employed on the USAW boundary to avoid particle penetration. Afterward, the ISPH method with the USAW boundary is utilized to simulate several free surface flow problems. The enhancement of stability as well as the accuracy of the simulations is validated firstly by the dam break tests and further studied through examples of solitary wave propagation and liquid sloshing. The numerical results are compared with available experiment data or results from other numerical methods, verifying that the improved ISPH model with the USAW boundary in this work is highly suitable for simulating free surface flow problems.