Targeting viscous flows around solid body at high Reynolds numbers with the delta-plus-SPH model

To avoid the inception of tensile instability, the ? + -SPH scheme is modified by switching the momentum equation to a non-conservative formulation in those fluid regions characterized by negative pressure. The loss of conservation properties is shown to induce small errors, provided that the particle distribution is regular. The latter condition is ensured by implementing the Particle Shifting Technique (PST). The novel variant of the ? + -SPH is proved to be effective in preventing the onset of tensile instability in a number of challenging benchmark tests, as for example, flows past bluff bodies at high Reynolds numbers. Reference solutions for the benchmark cases are obtained through DVH and Navier-Stokes solvers. A final simulation characterized by a deforming body that resembles a fish-like swimming is used as a practical application of the ? + -SPH model in biological fluid mechanics.