Pavel Ryzhakov

Advances in the Particle Finite Element Method (PFEM) for Solving Coupled Problems in Engineering

We present some developments in the formulation of the Particle Finite Element Method (PFEM) for analysis of complex coupled problems on fluid and solid mechanics in engineering accounting for fluid-structure interaction and coupled thermal effects, material degradation and surface wear. The PFEM uses an updated Lagrangian description to model the motion of nodes (particles) in both the fluid and the structure domains. Nodes are viewed as material points which can freely move and even separate from the main analysis domain representing, for instance, the effect of water drops. A mesh connects the nodes defining the discretized domain where the governing equations are solved, as in the standard FEM. The necessary stabilization for dealing with the incompressibility of the fluid is introduced via the finite calculus (FIC) method. An incremental iterative scheme for the solution of the non linear transient coupled fluid-structure problem is described. The procedure for modelling frictional contact conditions at fluid-solid and solidsolid interfaces via mesh generation are described. A simple algorithm to treat soil erosion in fluid beds is presented. An straight forward extension of the PFEM to model excavation processes and wear of rock cutting tools is described. Examples of application of the PFEM to solve a wide number of coupled problems in engineering such as the effect of large waves on breakwaters and bridges, the large motions of floating and submerged bodies, bed erosion in open channel flows, the wear of rock cutting tools during excavation and tunneling and the melting, dripping and burning of polymers in fire situations are presented.

A Monolithic FE Formulation for the Analysis of Membranes in Fluids

We propose here an efficient approach for treating the interaction between membranes and fluids. Slight compressibility of the fluid is assumed. Classical total Lagrangian formulation including wrinkling is adopted for the membrane representation, whereas fluid is treated in an updated Lagrangian manner, developed in the current work. Assumption of slight compressibility of the fluid enables one to define the monolithic fluid-membrane system in a natural way. The displacements are the primary variables of both the fluid and the membrane domains. The formulation adopts the Particle Finite Element Method (PFEM) philosophy for free-surface identification and mesh regeneration. Three examples illustrate the functionality of the formulation in application to FSI problems involving motion of membranes in water.

An implicit surface tension model for the analysis of droplet dynamics

Abstract A Lagrangian incompressible fluid flow model is extended by including an implicit surface tension term in order to analyze droplet dynamics. The Lagrangian framework is adopted to model the fluid and track its boundary, and the implicit surface tension term is used to introduce the appropriate forces at the domain boundary. The introduction of the tangent matrix corresponding to the surface tension force term ensures enhanced stability of the derived model. Static, dynamic and sessile droplet examples are simulated to validate the model and evaluate its performance. Numerical results are capable of reproducing the pressure distribution in droplets, and the advancing and receding contact angles evolution for droplets in varying substrates and inclined planes. The model is stable even at time steps up to 20 times larger than previously reported in literature and achieves first and second order convergence in time and space, respectively. The present implicit surface tension implementation is applicable to any model where the interface is represented by a moving boundary mesh.