Lagrangian analysis of multiscale particulate flows with the particle finite element method

Abstract

We present a Lagrangian numerical technique for the analysis of flows incorporating physical particles of different sizes. The numerical approach is based on the particle finite element method (PFEM) which blends concepts from particle-based techniques and the FEM. The basis of the Lagrangian formulation for particulate flows and the procedure for modelling the motion of small and large particles that are submerged in the fluid are described in detail. The numerical technique for analysis of this type of multiscale particulate flows using a stabilized mixed velocity-pressure formulation and the PFEM is also presented. Examples of application of the PFEM to several particulate flows problems are given.

A FEM-DEM technique for studying the motion of particles in non-Newtonian fluids. Application to the transport of drill cuttings in wellbores

“…(41) and (42) for homogeneous Lagrangian fluids can be found in [16]. Their applications in the context of particulate Newtonian Lagrangian fluids is presented in [4].…”

“…The coupling effects between the particles and the fluid are introduced via an immersed technique [3][4][5]. The fluid motion is modelled either with an Eulerian stabilized FEM formulation using a fixed mesh, or using a Lagrangian formulation using the Particle Finite Element Method (PFEM) [4,[6][7][8][9][10][11][12][13][14][15][16] for which the mesh evolves in time. For both the Eulerian and the Lagrangian formulations we use a mixed finite element formulation with an equal order linear interpolation for the velocities and the pressure variables.…”

“…Particleto-fluid forces have equal magnitude and opposite direction as the fluid-to-particle ones and are transferred to the fluid points as an additional body force vector in the momentum equations ( Figure 2). These forces, as well as the mass balance equations account for the percentage of particles in the fluid, similarly as it is done in immersed approaches for particulate flows [4,5,17]. The rest of the interaction forces between fluid and particles are neglected (lift forces, virtual mass forces, drag torque, etc.)…”

On the thermal response of a surface deposited laser-irradiated powder particle

“…We refer the reader to Duran [28], Pö schel and Schwager [29], Onate et al [30][31][32], Rojek et al [33,34], Carbonell et al [35], Labra and Onate [36], Leonardi et al [37], Cante et al [38], Bolintineanu et al [39], Avci and Wriggers [40] and Zohdi [41][42][43][44][45][46][47][48][49][50][51] for more computationallyoriented techniques aligned with manufacturing processes involving particles.…”

Numerical modelling of landslide-generated waves with the particle finite element method (PFEM) and a non-Newtonian flow model

“…5-7], although fully 3D approaches have sometimes been used, such as the smooth particle hydrodynamics method [2]. Ward and Day [8,9] presented the simplified 'tsunami balls' method, based on particles representing wave energy, and applied it to simulate landslide case studies at full scale.The phenomenon of landslide-generated waves is a paradigmatic example of fluid-soil-structure interaction problems, for whose analysis advanced numerical methods have been developed by the authors' groups [10][11][12]. More precisely, the authors have implemented a particular class of Lagrangian formulation for solving problems involving complex interactions between free surface fluids and solids.…”