Unsteady Vector Fields Research Articles

TSR-VFD: Generating temporal super-resolution for unsteady vector field data

We present TSR-VFD, a novel deep learning solution that recovers temporal super-resolution (TSR) of three-dimensional vector field data (VFD) for unsteady flow. In scientific visualization, TSR-VFD is the first work that leverages deep neural nets to interpolate intermediate vector fields from temporally sparsely sampled unsteady vector fields. The core of TSR-VFD lies in using two networks: InterpolationNet and MaskNet, that process the vector components of different scales from sampled vector fields as input and jointly output synthesized intermediate vector fields. To demonstrate our approach’s effectiveness, we report qualitative and quantitative results with several data sets and compare TSR-VFD against vector field interpolation using linear interpolation (LERP), generative adversarial network (GAN), and recurrent neural network (RNN). In addition, we compare TSR-VFD with a lossy compression (LC) scheme. Finally, we conduct a comprehensive study to evaluate critical parameter settings and network designs.

Capturing the dance of the earth: PolarGlobe: Real-time scientific visualization of vector field data to support climate science

This paper introduces a streamline visualization technique that empowers PolarGlobe, an interactive, virtual globe-based, multi-dimensional scientific visualization tool to facilitate the observation and visual inspection of changes in the climate in real time. Specifically, this technique achieves effective visualization of vector-based earth science data through an automated data processing pipeline which integrates novel strategies including random seeding, finer-granularity parallelization and real-time rendering. The random seeding strategy allows for a vivid visual effect and an interactive framerate regardless of the spatial resolution in the raw dataset. The visualization algorithm is designed to be naturally parallelizable by partitioning the rendering tasks of unsteady vector field into multiple subtasks such that high-performance rendering can be realized. The platform is capable of taking either irregular or regular gridded data as input, and through the proposed data (re)projection pipeline, an automatic transformation of spatially enabled scientific data from the original data projection to the 3D globe-based virtual space is achieved. A series of experiments was conducted to identify the best configuration of rendering parameters to achieve the optimal rendering performance and visual effect. The results demonstrated the scalability and capability of the proposed PolarGlobe system to visualize big and unsteady vector flow data across different spatial and temporal scales. PolarGlobe implements former Vice President Al Gore's vision of a digital earth that enables scientists and citizens across the world to interactively study our planet. We expect the methods and techniques presented in this work to contribute significantly to both the scientific visualization and climate science communities.

Robust Reference Frame Extraction from Unsteady 2D Vector Fields with Convolutional Neural Networks

AbstractRobust feature extraction is an integral part of scientific visualization. In unsteady vector field analysis, researchers recently directed their attention towards the computation of near‐steady reference frames for vortex extraction, which is a numerically challenging endeavor. In this paper, we utilize a convolutional neural network to combine two steps of the visualization pipeline in an end‐to‐end manner: the filtering and the feature extraction. We use neural networks for the extraction of a steady reference frame for a given unsteady 2D vector field. By conditioning the neural network to noisy inputs and resampling artifacts, we obtain numerically stabler results than existing optimization‐based approaches. Supervised deep learning typically requires a large amount of training data. Thus, our second contribution is the creation of a vector field benchmark data set, which is generally useful for any local deep learning‐based feature extraction. Based on Vatistas velocity profile, we formulate a parametric vector field mixture model that we parameterize based on numerically‐computed example vector fields in near‐steady reference frames. Given the parametric model, we can efficiently synthesize thousands of vector fields that serve as input to our deep learning architecture. The proposed network is evaluated on an unseen numerical fluid flow simulation.

Vector Field Topology of Time-Dependent Flows in a Steady Reference Frame.

The topological analysis of unsteady vector fields remains to this day one of the largest challenges in flow visualization. We build up on recent work on vortex extraction to define a time-dependent vector field topology for 2D and 3D flows. In our work, we split the vector field into two components: a vector field in which the flow becomes steady, and the remaining ambient flow that describes the motion of topological elements (such as sinks, sources and saddles) and feature curves (vortex corelines and bifurcation lines). To this end, we expand on recent local optimization approaches by modeling spatially-varying deformations through displacement transformations from continuum mechanics. We compare and discuss the relationships with existing local and integration-based topology extraction methods, showing for instance that separatrices seeded from saddles in the optimal frame align with the integration-based streakline vector field topology. In contrast to the streakline-based approach, our method gives a complete picture of the topology for every time slice, including the steps near the temporal domain boundaries. With our work it now becomes possible to extract topological information even when only few time slices are available. We demonstrate the method in several analytical and numerically-simulated flows and discuss practical aspects, limitations and opportunities for future work.

A user-friendly interactive framework for unsteady fluid flow segmentation and visualization

While vector fields are essential to simulate a large amount of natural phenomena, the difficulty to identify patterns and predict behaviors makes the visual segmentation in simulations an attractive and powerful tool. In this paper, we present a novel user-steered segmentation framework to cope with steady as well as unsteady vector fields on fluid flow simulations. Given a discrete vector field, our approach extracts multi-valued features from the field by exploiting its streamline structures so that these features are mapped to a visual space through a multidimensional projection technique. From an easy-to-handle interface, the user can interact with the projected data so as to partition and explore the most relevant vector features in a guidance frame of the simulation. Besides navigating and visually mining structures of interest, the interactivity with the projected data also allows the user to progressively enhance the segmentation result according to his insights. Finally, to successfully deal with unsteady simulations, the segments previously annotated by the user are used as a training set for a Support Vector Machine approach that classifies the remaining frames in the flow. We attest the effectiveness and versatility of our methodology throughout a set of classical physical-inspired applications on fluid flow simulations as depicted in the experiment results section.

UIA: a uniform integrated advection algorithm for steady and unsteady piecewise linear flow field on structured and unstructured grids

Integration-based geometric method is widely used in vector field visualization. To improve the efficiency of integration advection-based visualization, we propose a uniform integrated advection (UIA) algorithm on steady and unsteady vector field according to common piecewise linear field data set analysis. UIA employs cell gradient-based interpolation along spatial and temporal direction, and transforms multi-step advection into single-step advection in association with fourth-order Runge–Kutta advection process. UIA can significantly reduce computational load, and is applicable on arbitrary grid type with cell-center/cell-vertex data structure. The experiments are performed on steady/unsteady vector fields with two-dimensional cell-center unstructured grids and three-dimensional cell-vertex grids, and also on unsteady field from fluid dynamics numerical simulation. The result shows that the proposed algorithm can significantly improve advection efficiency and reduce visualization computational time compared with fourth-order Runge–Kutta.

Backward Finite-Time Lyapunov Exponents in Inertial Flows.

Inertial particles are finite-sized objects that are carried by fluid flows and in contrast to massless tracer particles they are subject to inertia effects. In unsteady flows, the dynamics of tracer particles have been extensively studied by the extraction of Lagrangian coherent structures (LCS), such as hyperbolic LCS as ridges of the Finite-Time Lyapunov Exponent (FTLE). The extension of the rich LCS framework to inertial particles is currently a hot topic in the CFD literature and is actively under research. Recently, backward FTLE on tracer particles has been shown to correlate with the preferential particle settling of small inertial particles. For larger particles, inertial trajectories may deviate strongly from (massless) tracer trajectories, and thus for a better agreement, backward FTLE should be computed on inertial trajectories directly. Inertial backward integration, however, has not been possible until the recent introduction of the influence curve concept, which - given an observation and an initial velocity - allows to recover all sources of inertial particles as tangent curves of a derived vector field. In this paper, we show that FTLE on the influence curve vector field is in agreement with preferential particle settling and more importantly it is not only valid for small (near-tracer) particles. We further generalize the influence curve concept to general equations of motion in unsteady spatio-velocity phase spaces, which enables backward integration with more general equations of motion. Applying the influence curve concept to tracer particles in the spatio-velocity domain emits streaklines in massless flows as tangent curves of the influence curve vector field. We demonstrate the correlation between inertial backward FTLE and the preferential particle settling in a number of unsteady vector fields.

Robustness-Based Simplification of 2D Steady and Unsteady Vector Fields.

Vector field simplification aims to reduce the complexity of the flow by removing features in order of their relevance and importance, to reveal prominent behavior and obtain a compact representation for interpretation. Most existing simplification techniques based on the topological skeleton successively remove pairs of critical points connected by separatrices, using distance or area-based relevance measures. These methods rely on the stable extraction of the topological skeleton, which can be difficult due to instability in numerical integration, especially when processing highly rotational flows. In this paper, we propose a novel simplification scheme derived from the recently introduced topological notion of robustness which enables the pruning of sets of critical points according to a quantitative measure of their stability, that is, the minimum amount of vector field perturbation required to remove them. This leads to a hierarchical simplification scheme that encodes flow magnitude in its perturbation metric. Our novel simplification algorithm is based on degree theory and has minimal boundary restrictions. Finally, we provide an implementation under the piecewise-linear setting and apply it to both synthetic and real-world datasets. We show local and complete hierarchical simplifications for steady as well as unsteady vector fields.

Vortex Cores of Inertial Particles.

The cores of massless, swirling particle motion are an indicator for vortex-like behavior in vector fields and to this end, a number of coreline extractors have been proposed in the literature. Though, many practical applications go beyond the study of the vector field. Instead, engineers seek to understand the behavior of inertial particles moving therein, for instance in sediment transport, helicopter brownout and pulverized coal combustion. In this paper, we present two strategies for the extraction of the corelines that inertial particles swirl around, which depend on particle density, particle diameter, fluid viscosity and gravity. The first is to deduce the local swirling behavior from the autonomous inertial motion ODE, which eventually reduces to a parallel vectors operation. For the second strategy, we use a particle density estimation to locate inertial attractors. With this, we are able to extract the cores of swirling inertial particle motion for both steady and unsteady 3D vector fields. We demonstrate our techniques in a number of benchmark data sets, and elaborate on the relation to traditional massless corelines.

Application of the Shannon-Kotelnik theorem on the vortex structures identification

This paper presents a decomposition of unsteady vector fields, based on the principle of Shannon-Kotelnik theorem. The decomposition is derived from the Fourier transform of the Kotelnik series. The method can be used for the analysis of both forced and self-excited oscillation.

Time‐Dependent 2‐D Vector Field Topology: An Approach Inspired by Lagrangian Coherent Structures

Abstract This paper presents an approach to a time‐dependent variant of the concept of vector field topology for 2‐D vector fields. Vector field topology is defined for steady vector fields and aims at discriminating the domain of a vector field into regions of qualitatively different behaviour. The presented approach represents a generalization for saddle‐type critical points and their separatrices to unsteady vector fields based on generalized streak lines, with the classical vector field topology as its special case for steady vector fields. The concept is closely related to that of Lagrangian coherent structures obtained as ridges in the finite‐time Lyapunov exponent field. The proposed approach is evaluated on both 2‐D time‐dependent synthetic and vector fields from computational fluid dynamics.

Computation of Localized Flow for Steady and Unsteady Vector Fields and Its Applications

We present, extend, and apply a method to extract the contribution of a subregion of a data set to the global flow. To isolate this contribution, we decompose the flow in the subregion into a potential flow that is induced by the original flow on the boundary and a localized flow. The localized flow is obtained by subtracting the potential flow from the original flow. Since the potential flow is free of both divergence and rotation, the localized flow retains the original features and captures the region-specific flow that contains the local contribution of the considered subdomain to the global flow. In the remainder of the paper, we describe an implementation on unstructured grids in both two and three dimensions for steady and unsteady flow fields. We discuss the application of some widely used feature extraction methods on the localized flow and describe applications like reverse-flow detection using the potential flow. Finally, we show that our algorithm is robust and scalable by applying it to various flow data sets and giving performance figures.

High-Quality and Interactive Animations of 3D Time-Varying Vector Fields

In this paper, we present an interactive texture-based method for visualizing three-dimensional unsteady vector fields. The visualization method uses a sparse and global representation of the flow, such that it does not suffer from the same perceptual issues as is the case for visualizing dense representations. The animation is made by injecting a collection of particles evenly distributed throughout the physical domain. These particles are then tracked along their path lines. At each time step, these particles are used as seed points to generate field lines using any vector field such as the velocity field or vorticity field. In this way, the animation shows the advection of particles while each frame in the animation shows the instantaneous vector field. In order to maintain a coherent particle density and to avoid clustering as time passes, we have developed a novel particle advection strategy which produces approximately evenly-spaced field lines at each time step. To improve rendering performance, we decouple the rendering stage from the preceding stages of the visualization method. This allows interactive exploration of multiple fields simultaneously, which sets the stage for a more complete analysis of the flow field. The final display is rendered using texture-based direct volume rendering.

Dense texture-based visualization of unsteady and multi-variate vector fields

We propose a novel technique that allows producing dense smooth visualization of unsteady vector fields. The suggested algorithm is texture-based: the field, which may depend on various quantities, such as time, determines how a chosen basic pattern of a texture has to be transformed and adapted to locally represent the features and variation of the field. Texture synthesis methods that aim at generating globally smooth textures yield dense visualizations of the vector field. Extending this synthesis in time leads to texture-based animations with frame-to-frame coherence. This approach is general and produces unsteady field visualizations in an intuitive and straightforward way. Additional degrees of freedom offer ways for user intervention (e.g. filtering and blending) or taking into consideration perception issues. This also makes this methodology useful and adaptable for a broad range of applications.

Interactive visualization of three-dimensional vector fields with flexible appearance control

In this paper, we present an interactive texture-based algorithm for visualizing three-dimensional steady and unsteady vector fields. The goal of the algorithm is to provide a general volume rendering framework allowing the user to compute three-dimensional flow textures interactively and to modify the appearance of the visualization on the fly. To achieve our goal, we decouple the visualization pipeline into two disjoint stages. First, flow lines are generated from the 3D vector data. Various geometric properties of the flow paths are extracted and converted into a volumetric form using a hardware-assisted slice sweeping algorithm. In the second phase of the algorithm, the attributes stored in the volume are used as texture coordinates to look up an appearance texture to generate both informative and aesthetic representations of the vector field. Our algorithm allows the user to interactively navigate through different regions of interest in the underlying field and experiment with various appearance textures. With our algorithm, visualizations with enhanced structural perception using various visual cues can be rendered in real time. A myriad of existing geometry-based and texture-based visualization techniques can also be emulated.

Interactive simulation and visualization of massless, massed, and evaporating particles

Most software packages available for particle tracing focus on visualizing steady or unsteady vector fields by using massless particle trajectories. For many applications, however, the use of massed and evaporating particles would provide a model of physical processes that could be used in product testing or design. In this article we describe the TrackPack toolkit, which provides an integrated interface for computing massless, massed, and evaporating particle trajectories in steady flow. In all cases, we assume a noncoupled model and compute particle trajectories through an existing vector field by numerically integrating with forward Euler, fourth-order Runge-Kutta, or an analytic streamline calculation. The TrackPack software effort was motivated by an industrial application to model pollution control systems in industrial boilers. We briefly describe the project and the visualization environment, and we demonstrate the necessity for massed, evaporating models in the application.

Interactive simulation and visualization of massless, massed, and evaporating particles

Most software packages available for particle tracing focus on visualizing steady or unsteady vector fields by using massless particle trajectories. For many applications, however, the use of massed and evaporating particles would provide a model of physical processes that could be used in product testing or design. In this article we describe the TrackPack toolkit, which provides an integrated interface for computing massless, massed, and evaporating particle trajectories in steady flow. In all cases, we assume a noncoupled model and compute particle trajectories through an existing vector field by numerically integrating with forward Euler, fourth-order Runge-Kutta, or an analytic streamline calculation. The TrackPack software effort was motivated by an industrial application to model pollution control systems in industrial boilers. We briefly describe the project and the visualization environment, and we demonstrate the necessity for massed, evaporating models in the application.

An Analysis of 3D Particle Path Integration Algorithms

Several techniques for the numerical integration of particle paths in steady and unsteady vector (velocity) fields are analyzed. Most of the analysis applies to unsteady vector fields, however, some results apply to steady vector field integration. Multistep, multistage, and some hybrid schemes are considered. It is shown that due to initialization errors, many unsteady particle path integration schemes are limited to third-order accuracy in time. Multistage schemes require at least three times more internal data storage than multistep schemes of equal order. However, for timesteps within the stability bounds, multistage schemes are generally more accurate. A linearized analysis shows that the stability of these integration algorithms are determined by the eigenvalues of the local velocity tensor. Thus, the accuracy and stability of the methods are interpreted with concepts typically used in critical point theory. This paper shows how integration schemes can lead to erroneous classification of critical points when the timestep is finite and fixed. For steady velocity fields, we demonstrate that timesteps outside of the relative stability region can lead to similar integration errors. From this analysis, guidelines for accurate timestep sizing are suggested for both steady and unsteady flows. In particular, using simulation data for the unsteady flow around a tapered cylinder, we show that accurate particle path integration requires timesteps which are at most on the order of the physical timescale of the flow.