Abstract

Particles are used to simulate phenomena spanning twenty orders of magnitude, from the folding of proteins to the formation of our universe. I distinguish particle methods for the discretisation of continuum conservation laws and particle models of complex systems. In this talk, I will emphasize the need for controlling the accuracy of continuum particle methods and demonstrate how particle remeshing allows for a seamless integration of grids and particles. I will also discuss the need for data driven, uncertainty quantification of particle models. I will provide examples from the capabilities and challenges for particle methods through flow simulations in massively parallel computing architectures, ranging from fish swimming and cavitation to cell sorting in microfluidic channels.

Abstract

The possibility to use a Lagrangian frame to solve problems with large time-steps was successfully explored previously by the authors for the solution of homogeneous incompressible fluids and also for solving multi-fluid problems [28-30]. The strategy used by the authors was named Particle Finite Element Method second generation (PFEM-2). The objective of this paper is to demonstrate in which circumstances the use of a Lagrangian frame with particles is more accurate than a classical Eulerian finite element method, and when large time-steps and/or coarse meshes may be used.

Abstract

Particle Methods are those in which the problem is represented by a discrete number of particles. Each particle moves accordingly with its own mass and the external/internal forces applied to it. Particle Methods may be used for both, discrete and continuous problems. In this paper, a Particle Method is used to solve the continuous fluid mechanics equations. To evaluate the external applied forces on each particle, the incompressible Navier–Stokes equations using a Lagrangian formulation are solved at each time step. The interpolation functions are those used in the Meshless Finite Element Method and the time integration is introduced by an implicit fractional‐step method. In this manner classical stabilization terms used in the momentum equations are unnecessary due to lack of convective terms in the Lagrangian formulation. Once the forces are evaluated, the particles move independently of the mesh. All the information is transmitted by the particles. Fluid–structure interaction problems including free‐fluid‐surfaces, breaking waves and fluid particle separation may be easily solved with this methodology. 

Abstract

An advancing front technique for filling space with arbitrary, separated objects has been developed. The input required consists of the specification of the desired object type, the mean object size, the distance between objects in space, as well as an initial triangulation of the surface. The objects are assumed to be described by a coarse mesh of tetrahedra. One face at a time is removed from the active front, and, if possible, surrounded by admissible new objects. This operation is repeated until no active faces are left. Two techniques to obtain maximum packing are discussed: closest object placement (during generation) and move/enlarge (after generation). Several examples are included that demonstrate the capabilities of the technique. Copyright © 2009 John Wiley & Sons, Ltd.

Abstract

In this paper, we present a computational algorithm for solving an important practical problem, namely, the thermoplastic polymer melting under fire conditions. We propose here a technique that aims at minimizing the computational cost. This is basically achieved by using the immersed boundary‐like approach, combining the particle finite element method for the polymer with an Eulerian formulation for the ambience. The polymer and ambience domains interact over the interface boundary. The boundary is explicitly defined by the position of the Lagrangian domain (polymer) within the background Eulerian mesh (ambience). This allows to solve the energy equation for both subdomains on the Eulerian mesh with different thermal properties. Radiative transport equation is exclusively considered for the ambience, and the heat exchange at the interface is modeled by calculating the radiant heat flux and imposing it as a natural boundary condition.

Abstract

In this work a stabilized mixed formulation for the solution of non-linear solid mechanics problems in nearly-incompressible conditions is presented. In order to deal with high material deformation, an implicit Material Point Method is chosen. Such choice allows avoiding the classical limitations of the Finite Element Method, e.g., element tangling and extreme mesh distortion. The proposed mixed formulation, with displacement and pressure as primary variables, is tested through classical benchmarks in solid and geo-mechanics where a Neo-Hookean, a J2 and a Mohr-Coulomb plastic law are employed. Further, the stabilized mixed formulation is compared with a displacement-based formulation to demonstrate how the proposed approach gets better results in terms of accuracy, not only when incompressible materials are simulated, but also in the case of compressible ones.

Abstract

A methodology to integrate geographical information system (GIS) data with large-scale pedestrian simulations has been developed. Advances in automatic data acquisition and archiving from GIS databases, automatic input for pedestrian simulations, as well as scalable pedestrian simulation tools have made it possible to simulate pedestrians at the individual level for complete cities in real time. An example that simulates the evacuation of the city of Barcelona demonstrates that this is now possible. This is the first step towards a fully integrated crowd prediction and management tool that takes into account not only data gathered in real time from cameras, cell phones or other sensors, but also merges these with advanced simulation tools to predict the future state of the crowd.

Abstract

Multifluids are those fluids in which their physical properties (viscosity or density) vary internally and abruptly forming internal interfaces that introduce a large nonlinearity in the Navier–Stokes equations. For this reason, standard numerical methods require very small time steps in order to solve accurately the internal interface position. In a previous paper, the authors developed a particle‐based method (named particle finite element method (PFEM)) based on a Lagrangian formulation and FEM for solving the fluid mechanics equations for multifluids. PFEM was capable of achieving accurate results, but the limitation of small time steps was still present. In this work, a new strategy concerning the time integration for the analysis of multifluids is developed allowing time steps one order of magnitude larger than the previous method. The advantage of using a Lagrangian solution with PFEM is shown in several examples. All kind of heterogeneous fluids (with different densities or viscosities), multiphase flows with internal interfaces, breaking waves, and fluid separation may be easily solved with this methodology without the need of small time steps.

Abstract

Abstract