The Delta-ALE-SPH model: an improved Delta-SPH scheme containing particle shifting and ALE formulation

In the present work we derive a novel model, named Delta-ALE-SPH scheme, by merging the Delta-pluse- SPH scheme and the Arbitrary Lagrangian Eulerian (ALE) formulation. Differently from the Delta-plus-SPH scheme, the use of the ALE framework allows for an inclusion of the Particle Shifting Technique (PST) for recovering the consistency of particles' masses, volumes and positions. In the proposed scheme, a diffusive term is included in the density equation to ensure a regular pressure field. Furthermore, different constraints on the mass flux equation are investigated. Indeed we discovered that the accuracy of the solution as well as the properties of the scheme strongly depend on how this equation is numerically handled. Suitable algorithms for the numerical treatment near the free surface and on the solid wall boundary are implemented. These treatments improve the particle distribution and the pressure evaluation close to the fluid boundary. Finally, the Delta-ALE-SPH scheme is tested against several challenging benchmark test cases, proving to be more robust and accurate than the other SPH schemes.