Generalized-alpha 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 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. Firstly, it includes a detailed implementation analysis of the Generalized-alpha method in PFEM. The work recognizes and compares different implementation approaches from the literature, which differ mainly in the terms that are alpha-interpolated (state variables or forces of momentum equation) and the type of treatment for the pressure in the time integration scheme. Secondly, the work compares the performance of the Generalized-alpha method against the Backward Euler and Newmark schemes for the solution of the incompressible Navier-Stokes equations. Thirdly, 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.