Lagrangian analysis of multiscale particulate flows with particle finite element method

The study of fluid ows containing particles of different sizes (hereafter called particulate ows) is relevant to many areas of engineering and applied sciences. In this work we are concerned with particulate flows containing small to large particles. This type of ows is typical in slurry ows originated by natural hazards such as foods, tsunamis and landslides, as well as in many processes of the bio-medical and pharmaceutical industries, in the manufacturing industry and in the oil and gas industry (i.e. cuttings transport in boreholes), among other applications [1, 2, 6, 13, 14, 16, 21{23, 26, 47, 50, 51, 55, 61, 62]. Our interest in this work is the modelling and simulation of free surface particulate quasi-incompressible ows containing particles of different sizes using a particular class of Lagrangian FEM termed the Particle Finite Element Method (PFEM, www.cimne.com/pfem) [4, 5, 8, 11, 17{20, 25, 27, 28, 35, 36, 38, 40, 42{ 46]. The PFEM treats the mesh nodes in the uid and solid domains as particles which can freely move and even separate from the main uid domain. A mesh connects the nodes discretizing the domain where the governing equations are solved using a stabilized FEM. In Lagrangian analysis procedures (such as the PFEM) the motion of uid particles is tracked during the transient solution. Hence, the convective terms vanish in the momentum equations and no numerical stabilization is needed. Another source of instability, however, remains in the numerical solution of Lagrangian flows, that due to the treatment of the incompressibility constraint which requires using a stabilized numerical method.