Macroscopic modeling and simulations of room evacuation

We analyze numerically two macroscopic models of crowd dynamics: the classical Hughes model and the second order model being an extension to pedestrian motion of the Payne-Whitham vehicular traffic model. The desired direction of motion is determined by solving an eikonal equation with density dependent running cost, which results in minimization of the travel time and avoidance of congested areas. We apply a mixed finite volume-finite element method to solve the problems and present error analysis for the eikonal solver, gradient computation and the second order model yielding a first order convergence. We show that Hughes' model is incapable of reproducing complex crowd dynamics such as stop-and-go waves and clogging at bottlenecks. Finally, using the second order model, we study numerically the evacuation of pedestrians from a room through a narrow exit.Comment: 22 page

Metamodel-assisted particle swarm optimization and application to aerodynamic shape optimization

Modern optimization methods like Genetic Algorithms (GAs) and Particle Swarm Optimization (PSO) have been found to be very robust and general for solving engineering design problems. They require the use of large population size and may suffer from slow convergence. Both of these lead to large number of function evaluations which can significantly increase the cost of the optimization. This is especially so in view of the increasing use of costly high fidelity analysis tools like CFD. Metamodels also known as surrogate models, are a cheaper alternative to costly analysis tools. In this work we construct radial basis function approximations and use them in conjunction with particle swarm optimization in an inexact pre-evaluation procedure for aerodynamic design. We show that the use of mixed evaluations by metamodels/CFD can significantly reduce the computational cost of PSO while yielding optimal designs as good as those obtained with the costly evaluation tool

Radial Basis Functions and Kriging Metamodels for Aerodynamic Optimization

Population-based optimization methods like genetic algorithms and particle swarm optimization are very general and robust but can be costly since they require large number of function evaluations. The costly function evaluations can be replaced by cheaper models which are refered to as surrogate or meta models. Here we consider data-fitting models, particularly radial basis functions and kriging. We study the performance of these interpolation models on some analytical functions and aerodynamic data. Both the models have parameters which must be selected carefully to ensure good accuracy. For RBF, we implement a leave-one-out validation technique and for kriging, the parameters are determined by maximizing the probability density of the available data using a particle swarm optimization. The metamodels are then implemented in the shape optimization platform FAMOSA

Low cost PSO using metamodels and inexact pre-evaluation: Application to aerodynamic shape design

International audienceModern optimization methods like Genetic Algorithms (GAs) and Particle Swarm Optimization (PSO) have been found to be very robust and general for solving engineering design problems. They require the use of large population size and may suffer from slow convergence. Both of these lead to large number of function evaluations which can significantly increase the computational cost. This is especially so in view of the increasing use of costly high fidelity analysis tools like Computational Fluid Dynamics (CFD). Metamodels also known as surrogate models, are a cheaper alternative to costly analysis tools. In this work we construct radial basis function approximations and use them in conjunction with particle swarm optimization in an inexact pre-evaluation procedure for aerodynamic design. We show that the use of mixed evaluations by metamodels/CFD can significantly reduce the computational cost of PSO while yielding optimal designs as good as those obtained with the costly evaluation tool

Geometric model for automated multi-objective optimization of foils

This paper describes a new generic parametric modeller integrated into an auto- mated optimization loop for shape optimization. The modeller enables the generation of shapes by selecting a set of design parameters that controls a twofold parameterization: geometrical - based on a skeleton approach - and architectural - based on the experience of practitioners - to impact the system performance. The resulting forms are relevant and effective, thanks to a smoothing procedure that ensures the consistency of the shapes produced. As an application, we propose to perform a multi-objective shape optimization of a AC45 foil. The modeller is linked to the fluid solver AVANTI, coupled with Xfoil, and to the optimization toolbox FAMOSA

Optimisation aérodynamique du conduit de refroidissement d'un véhicule Formula-E

The objective of this study is to simulate the flow in the cooling duct of a Formula-E vehicle, and then optimize the duct shape to maximize the flow rate. In this perspective, weconsider a radiator model defined as a porous medium, implemented in a Finite-Volume codebased on the resolution of Reynolds-averaged Navier-Stokes equations. A two-dimensional studyis conducted, including the quantification of discretization and modeling errors, to estimate theimpact of the different parameters related to the radiator and cooling duct geometry. Finally,the automated optimization of the most relevant parameters is achieved using a response surfacemethod.On souhaite dans cette étude simuler l’écoulement d’air dans le conduit de refroidissementd’un véhicule de type Formula-E, puis optimiser la forme du conduit pour maximiser ledébit. Dans cette perspective, on considère un modèle de radiateur de type "milieu poreux", prisen compte dans un code volumes-finis reposant sur la résolution des équations de Navier-Stokesen moyenne de Reynolds. Une étude bi-dimensionnelle est menée, incluant la quantification deserreurs de discrétisation et de modélisation, pour estimer l’impact des différents paramètres liésau radiateur et à la géométrie du conduit de refroidissement. Finalement, une optimisation automatiquedes paramètres les plus pertinents est réalisée avec un algorithme de type surfaces deréponse

Interactive design of 2D car profiles with aerodynamic feedback

International audienceThe design of car shapes requires a delicate balance between aesthetic and performance. While fluid simulation provides themeans to evaluate the aerodynamic performance of a given shape, its computational cost hinders its usage during the early explorative phases of design, when aesthetic is decided upon. We present an interactive system to assist designers in creating aerodynamic car profiles. Our system relies on a neural surrogate model to predict fluid flow around car shapes, providing fluid visualization and shape optimization feedback to designers as soon as they sketch a car profile. Compared to prior work that focused on time-averaged fluid flows, we describe how to train our model on instantaneous, synchronized observations extracted from multiple pre-computed simulations, such that we can visualize and optimize for dynamic flow features, such as vortices. Furthermore, we architectured our model to support gradient-based shape optimization within a learned latent space of car profiles. In addition to regularizing the optimization process, this latent space and an associated encoder-decoder allows us to input and output car profiles in a bitmap form, without any explicit parameterization of the car boundary. Finally, we designed our model to support pointwise queries of fluid properties around car shapes, allowing us to adapt computational cost to application needs. As an illustration, we only query our model along streamlines for flow visualization, we query it in the vicinity of the car for drag optimization, and we query it behind the car for vortex attenuation

Aerodynamic Shape Optimization using a Full and Adaptive Multilevel Algorithm

International audienceWe are interested by the general problem consisting of minimizing a functional of a state field solution of a PDE state equation. In Particular in this work, we optimize a 3D wing shape immersed an in inviscid flow to reduce drag. Whence, each evaluation of the cost functional is computationally expensive. For improving the convergence rate of the optimization algorihm, we propose a multi-scale algorithm inspired from the Full Multi-Grid method [1], and referred to as the Full and Adaptive Multi-Level Optimum-Shape Algorithm (FAMOSA), originally defined in [5]. The proposed method include the following strategies: • The simplest scheme " one way up " by choosing the parametrization of Bézier type to construct a hierarchy of embedded parametric spaces, via the classical degree elevation process [3]. • V-cycle algorithm by using (on the coarse level) " perturbation " unknowns from the latest fine estimate, i.e deformation instead of shapes

Comparative Study of Macroscopic Pedestrian Models

International audienceWe analyze numerically some macroscopic models of pedestrian motion to compare their capabilities of reproducing characteristic features of crowd behavior, such as travel times minimization and crowded zones avoidance, as well as complex dynamics like stop-and-go waves and clogging at bottlenecks. We compare Hughes’ model with different running costs, a variant with local dependency on the density gradient proposed in Xia et al. (2009), and a second order model derived from the Payne-Whitham traffic model which has first been analyzed in Jiang et al. (2010). In particular, our study shows that first order models are incapable of reproducing stop-and-go waves and blocking at exits

Multi-niveaux de modèles

National audienc