Numerical studies to propose a ghost particle removed SPH (GR-SPH) method

This paper aims to propose a new modified SPH method with novel treatments at the boundaries. Although SPH methods decrease contradictions due to grid distortions compared to traditional mesh-based methods, the penetration of particles through boundaries and the consistency problem make the simulation of problems with definite boundaries a concern. The use of ghost boundary particles and the insertion of artificial forces at the boundaries are the most popular boundary consistency treatments proposed thus far. The use of artificial forces causes the mixing of molecular and finite theories, which can violate the conservation of momentum. This paper shows how the use of ghost boundary particles can violate the continuity equation in problems with non-zero velocity divergence. This study proposes a novel ghost particle removed SPH (GR-SPH) method that discards all ghost particles and artificial forces at the boundaries. Liner layers and liner particles have been defined inside the domain instead of ghost boundary particles in such a way that the so-called violations can partially be remedied. Based on the continuity equation and kernel function unity specification, a novel truncation correction factor has been defined for density renormalization to override the consistency problem at the boundaries. In addition, a new method is proposed to detect the particles near complex wall boundaries and evaluate the normal distance from boundaries. Finally, some benchmark problems have been solved to show the capabilities of the new modified SPH method for the prediction of both particle location and pressure distribution with acceptable accuracy. The GR-SPH method facilitates programming, with fewer particles contributing to the computations. Comparison of its outcomes with published results shows that the new treatments executed at the boundaries are effective.