Trajectory-Based Analysis of Flow Simulation Data
Mathias Hummel · Publication Server of Kaiserslautern University of Technology (Kaiserslautern University of Technology) · 2019
The simulation of physical phenomena involving the dynamic behavior of fluids and gases has numerous applications in various fields of science and engineering. Of particular interest is the material transport behavior, the tendency of a flow field to displace parts of the medium. Therefore, many visualization techniques rely on particle trajectories. Lagrangian Flow Field Representation. In typical Eulerian settings, trajectories are computed from the simulation output using numerical integration schemes. Accuracy concerns arise because, due to limitations of storage space and bandwidth, often only a fraction of the computed simulation time steps are available. Prior work has shown empirically that a Lagrangian, trajectory-based representation can improve accuracy [Agr+14]. Determining the parameters of such a representation in advance is difficult; a relationship between the temporal and spatial resolution and the accuracy of resulting trajectories needs to be established. We provide an error measure for upper bounds of the error of individual trajectories. We show how areas at risk for high errors can be identified, thereby making it possible to prioritize areas in time and space to allocate scarce storage resources. Comparative Visual Analysis of Flow Field Ensembles. Independent of the representation, errors of the simulation itself are often caused by inaccurate initial conditions, limitations of the chosen simulation model, and numerical errors. To gain a better understanding of the possible outcomes, multiple simulation runs can be calculated, resulting in sets of simulation output referred to as ensembles. Of particular interest when studying the material transport behavior of ensembles is the identification of areas where the simulation runs agree or disagree. We introduce and evaluate an interactive method that enables application scientists to reliably identify and examine regions of agreement and disagreement, while taking into account the local transport behavior within individual simulation runs. Particle-Based Representation and Visualization of Uncertain Flow Data Sets. Unlike simulation ensembles, where uncertainty of the solution appears in the form of different simulation runs, moment-based Eulerian multi-phase fluid simulations are probabilistic in nature. These simulations, used in process engineering to simulate the behavior of bubbles in liquid media, are aimed toward reducing the need for real-world experiments. The locations of individual bubbles are not modeled explicitly, but stochastically through the properties of locally defined bubble populations. Comparisons between simulation results and physical experiments are difficult. We describe and analyze an approach that generates representative sets of bubbles for moment-based simulation data. Using our approach, application scientists can directly, visually compare simulation results and physical experiments.