Modified Finite Particle Methods for Stokes problems

The Modified Finite Particle Method (MFPM) is a numerical method belonging to the class of meshless methods, nowadays widely investigated due to their characteristic of being capable to easily model large deformation and fluid-dynamic problems. Here we use the MFPM to approximate the Stokes problem. Since the classical formulation of the Stokes problem may lead to pressure spurious oscillations, we investigate alternative formulations and focus on how MFPM discretization behaves in those situations. Some of the investigated formulations, in fact, do not enforce strongly the incompressibility constraint, and therefore an important issue of the present work is to verify if the MFPM is able to correctly reproduce the incompressibility in those cases. The numerical results show that for the formulations in which the incompressibility constraint is properly satisfied from a numerical point of view, the expected second-order is achieved, both in static and in dynamic problems.