Generalized-α scheme in the PFEM for velocity-pressure and displacement-pressure formulations of the incompressible Navier-Stokes equations

Despite the increasing use of the particle finite element method (PFEM) in fluid flow simulation and the outstanding success of the Generalized-alpha$$ \alpha $$ (GA) time integration method, very little discussion has been devoted to their combined performance. This work aims to contribute in this regard by addressing three main aspects. First, it includes a detailed implementation analysis of the GA method in PFEM. The work recognizes and compares different implementation approaches from the literature, which differ mainly in the terms that are alpha$$ \alpha $$-interpolated (state variables or forces of momentum equation) and the type of treatment for the pressure in the time integration scheme. Second, the work compares the performance of the GA method against the Backward Euler and Newmark schemes for the solution of the incompressible Navier-Stokes equations. Third, the study is enriched by considering not only the classical velocity-pressure formulation but also the displacement-pressure formulation that is gaining interest in the fluid-structure interaction field. The work is carried out using various 2D and 3D benchmark problems such as the fluid sloshing, the solitary wave propagation, the flow around a cylinder, and the collapse of a cylindrical water column.