Steady State of Pedestrian Flow in Bottleneck Experiments

Experiments with pedestrians could depend strongly on initial conditions. Comparisons of the results of such experiments require to distinguish carefully between transient state and steady state. In this work, a feasible algorithm - Cumulative Sum Control Chart - is proposed and improved to automatically detect steady states from density and speed time series of bottleneck experiments. The threshold of the detection parameter in the algorithm is calibrated using an autoregressive model. Comparing the detected steady states with previous manually selected ones, the modified algorithm gives more reproducible results. For the applications, three groups of bottleneck experiments are analysed and the steady states are detected. The study about pedestrian flow shows that the difference between the flows in all states and in steady state mainly depends on the ratio of pedestrian number to bottleneck width. When the ratio is higher than a critical value (approximately 115 persons/m), the flow in all states is almost identical with the flow in steady state. Thus we have more possibilities to compare the flows from different experiments, especially when the detection of steady states is difficult.Comment: 19 pages, 7 figure

dgfire - Smoke and fire simulations with hp-adaptive Discontinuous Galerkin Methods

Over the last decade, CFD simulations in fire safety have gained a large amount of attention; in both the scientific field and engineering application. At the same time many modern CFD techniques, like unstructured adaptive grids, high accuracy methods and efficiently scalable solver (on thousands of computer cores) [1], have become available for practical applications. In contrast to simulations using static meshes, adaptive methods allow for a more efficient use of computing time. Based on refinement criteria, e.g. solution quality, turbulence resolution [4], or inversion layers, an adaptive mesh can be locally modified – i.e. refined or coarsened to achieve the favored quality criteria, without increasing the global resolution. This approach does not require any a-priori knowledge of the movement of smoke or fire to adopt the computational grid. Applying this method to existing fire simulation software would cause a massive reorganization of existing code. We therefore setup a new simulation framework based on established numerical libraries. By taking advantage of external libraries, new methods and innovations can easily be adopted. To allow complex geometries, the Discontinuous Galerkin Method (DG) is chosen as discretization scheme, which is a variant of the Finite Element Method and suitable for hyperbolic flow problems. It features local conservation of preservation variables and is well suited for applications on massive parallel computers. DG can handle unstructured meshes with hanging nodes and is appropriate for hp-adaptivity. As h-adaptivity denotes the refinement of the grid itself, it allows the mesh to adopt itself geometrically to the quality criteria. The p-adaptivity reflects the change in the degree of the DG polynomial approximation. Especially for turbulent flows, the benefits of p-adaptivity are currently discussed [2]. The combination of both adaptions, i.e. hp-adaptivity, is shown to provide exponential convergence [3]. This enables high resolution fire simulations in complex environments within reasonable computing time. Since we are using higher order schemes in spatial dimension, a more elaborate handling of time is required. Here SDIRK4 is used, which is a 4th order singly-diagonally-implicit Runge-Kutta method [5], featuring adaptive time-stepping and continuous extension between current and future step to correct splitting errors. In the presented contribution towards adaptive smoke and fire simulations, we introduce the involved numerical and computational concepts and their implementations. Additionally, we demonstrate the use of adaptive grids for the prediction of smoke movement