Real-time visualization of unsteady vector fields

We propose unsteady flow advection-convolution (UFAC) as a novel visualization approach for unsteady flows. It performs time evolution governed by pathlines, but builds spatial correlation according to instantaneous streamlines whose spatial extent is controlled by the flow unsteadiness. UFAC is derived from a generic framework that provides spacetime-coherent dense representations of time dependent-vector fields by a two-step process: 1) construction of continuous trajectories in spacetime for temporal coherence; and 2) convolution along another set of paths through the above spacetime for spatially correlated patterns. Within the framework, known visualization techniques-such as Lagrangian-Eulerian advection, image-based flow visualization, unsteady flow LIC, and dynamic LIC-can be reproduced, often with better image quality, higher performance, or increased flexibility of the visualization style. Finally, we present a texture-based discretization of the framework and its interactive implementation on graphics hardware, which allows the user to gradually balance visualization speed against quality.

In this paper, we propose a new technique to visualize dense representations of time-dependent vector fields based on a Lagrangian-Eulerian Advection (LEA) scheme. The algorithm produces animations with high spatio-temporal correlation at interactive rates. With this technique, every still frame depicts the instantaneous structure of the flow, whereas an animated sequence of frames reveals the motion a dense collection of particles would take when released into the flow. The simplicity of both the resulting data structures and the implementation suggest that LEA could become a useful component of any scientific visualization toolkit concerned with the display of unsteady flows.

We present a technique for direct visualization of unsteady flow on surfaces from computational fluid dynamics. The method generates dense representations of time-dependent vector fields with high spatio-temporal correlation using both Lagrangian-Eulerian advection and image based flow visualization as its foundation. While the 3D vector fields are associated with arbitrary triangular surface meshes, the generation and advection of texture properties is confined to image space. Frame rates of up to 20 frames per second are realized by exploiting graphics card hardware. We apply this algorithm to unsteady flow on boundary surfaces of, large, complex meshes from computational fluid dynamics composed of more than 250,000 polygons, dynamic meshes with time-dependent geometry and topology, as well as medical data.

The analysis of data that consists of multiple vector fields can be greatly facilitated by the simultaneous visualization of the vector fields. An effective visualization must accurately reflect the key physical structures of the fields in a way that does not allow for an unintended bias toward one distribution. While there are several effective techniques to visualize a single vector field through equally spaced streamlines, applying these techniques to individual vector fields and combining them in a single image yields undesirable artifacts. In this paper, we present strategies for the effective visualization of two vector fields through the use of streamlines.

This paper describes an approach for interactive visualization of mixed scalar and vector fields, in which vector icons are generated from pre-voxelized icon templates and volume-rendered together with the volumetric scalar data. This approach displays simultaneously the global structure of the scalar field and the detailed features of the vector field. Interactive visualization is achieved with incremental image update, by re-rendering only a small portion of the image wherever and whenever a change occurs. This technique supports a set of interactive visualization tools, including change of vector field visualization parameters, real-time animation of vector icons advected within the scalar field, a zooming lens, and a local probe. Subject Terms: data visualisation; interactive systems; graphical user interfaces; rendering (computer graphics); interactive visualization; scalar fields; vector fields; vector icons; pre-voxelized icon templates; volume-rendered; volumetric scalar data; incremental image update; real-time animation; zooming lens; local probe

Streamline1 is one of the most widely used method in vector field visualization. However, with the expansion of data size, the existing methods cannot ensure the efficiency while maintaining high accuracy. In order to analyse the vector field efficiently, this paper proposes an algorithm for streamline visualization in unstructured vector field while keeping both efficiency and accuracy based on Kipfer's algorithm[1]. First, all grids are classified according to their Jordan canonical form. Then the streamline expressions in each grid cell are deduced for each kind of the grids, and we found that the expressions can be represented in a uniform way. Finally, the exit point of the streamline in the grid cell is calculated by solving the equation composed of the streamline expression and the equation of each face of the tetrahedron. The exit point can be obtained quickly and accurately by using Newton iterative method. The experimental results show that our algorithm is more efficient for streamline visualization with the same accuracy than Kipfer's algorithm.

It is a challenging task to visualize the behavior of time-dependent 3D vector fields. Most of the time an overview of unsteady fields is provided via animations, but, unfortunately, animations provide only transient impressions of momentary flow. In this paper we present two approaches to visualize time varying fields with fixed geometry. Path lines and streak lines represent such a steady visualization of unsteady vector fields, but because of occlusion and visual clutter it is useless to draw them all over the spatial domain. A selection is needed. We show how bundles of streak lines and path lines, running at different times through one point in space, like through an eyelet, yield an insightful visualization of flow structure (eyelet lines). To provide a more intuitive and appealing visualization we also explain how to construct a surface from these lines. As second approach, we use a simple measurement of local changes of a field over time to determine regions with strong changes. We visualize these regions with isosurfaces to give an overview of the activity in the dataset. Finally we use the regions as a guide for placing eyelets.

A new method for the simplification and the visualization of vector fields is presented based on the notion of centroidal Voronoi tessellations (CVT's). A CVT is a special Voronoi tessellation for which the generators of the Voronoi regions in the tessellation are also the centers of mass (or means) with respect to a prescribed density. A distance function in both the spatial and vector spaces is introduced to measure the similarity of the spatially distributed vector fields. Based on such a distance, vector fields are naturally clustered and their simplified representations are obtained. Our method combines simple geometric intuitions with the rigorously established optimality properties of the CVTs. It is simple to describe, easy to understand and implement. Numerical examples are also provided to illustrate the effectiveness and competitiveness of the CVT-based vector simplification and visualization methodology.

In this paper, we present a high-quality texture-based enhanced approach for the visualization of unsteady vector fields. It adopts a scheme of streamline enhancement by applying a ID high-pass filter to flow textures along the orthogonal flow direction to enhance the intensity contrast among streamlines and improve the image quality of flow textures. A scheme of boundary supplement is also used to modulate the characteristic of particles flow. Using the color mapping of some scalar properties, such as magnitude, orientation and curvature, it is capable of displaying many properties of vector field which are helpful to analyze the features and topological flow patterns. It is capable of achieving a real-time rendering performance on a personal computer by using current graphics hardware.

One major discipline of Scientific Visualization is the display of vector field data. We address the problem of visualizing vector fields containing critical points of higher order Poincare-Index. We use polynomial pieces so that the degree is high enough to get the right Poincare-Index at the location of the critical points. This is an essential improvement because nearly all visualization of vector fields up to now used piecewise linear interpolation and therefore can not show this kind of critical points. A description of vector fields in Clifford algebra opens the way to a better understanding of some plane polynomial vector fields. This is used to choose the polynomial approximations needed for the visualization.

Intelligent mobile sensors, such as uninhabited aerial or underwater vehicles, are becoming prevalent in environmental sensing and monitoring applications. These active sensing platforms operate in unsteady fluid flows, including windy urban environments, hurricanes, and ocean currents. Often constrained in their actuation capabilities, the dynamics of these mobile sensors depend strongly on the background flow, making their deployment and control particularly challenging. Therefore, efficient trajectory planning with partial knowledge about the background flow is essential for teams of mobile sensors to adaptively sense and monitor their environments. In this work, we investigate the use of finite-horizon model predictive control (MPC) for the energy-efficient trajectory planning of an active mobile sensor in an unsteady fluid flow field. We uncover connections between the finite-time optimal trajectories and finite-time Lyapunov exponents (FTLE) of the background flow, confirming that energy-efficient trajectories exploit invariant coherent structures in the flow. We demonstrate our findings on the unsteady double gyre vector field, which is a canonical model for chaotic mixing in the ocean. We present an exhaustive search through critical MPC parameters including the prediction horizon, maximum sensor actuation, and relative penalty on the accumulated state error and actuation effort. We find that even relatively short prediction horizons can often yield nearly energy-optimal trajectories. These results are promising for the adaptive planning of energy-efficient trajectories for swarms of mobile sensors in distributed sensing and monitoring.

We present the design of a scalable parallel pathline construction method for visualizing large time-varying 3D vector fields. A 4D (i.e., time and the 3D spatial domain) representation of the vector field is introduced to make a time-accurate depiction of the flow field. This representation also allows us to obtain pathlines through streamline tracing in the 4D space. Furthermore, a hierarchical representation of the 4D vector field, constructed by clustering the 4D field, makes possible interactive visualization of the flow field at different levels of abstraction. Based on this hierarchical representation, a data partitioning scheme is designed to achieve high parallel efficiency. We demonstrate the performance of parallel pathline visualization using data sets obtained from terascale flow simulations. This new capability will enable scientists to study their time-varying vector fields at the resolution and interactivity previously unavailable to them.

Vector field visualization techniques have evolved very rapidly over the last two decades, however, visualizing vector fields on complex boundary surfaces from computational flow dynamics (CFD) still remains a challenging task. In part, this is due to the large, unstructured, adaptive resolution characteristics of the meshes used in the modeling and simulation process. Out of the wide variety of existing flow field visualization techniques, vector field clustering algorithms offer the advantage of capturing a detailed picture of important areas of the domain while presenting a simplified view of areas of less importance. This paper presents a novel, robust, automatic vector field clustering algorithm that produces intuitive and insightful images of vector fields on large, unstructured, adaptive resolution boundary meshes from CFD. Our bottom-up, hierarchical approach is the first to combine the properties of the underlying vector field and mesh into a unified error-driven representation. The motivation behind the approach is the fact that CFD engineers may increase the resolution of model meshes according to importance. The algorithm has several advantages. Clusters are generated automatically, no surface parameterization is required, and large meshes are processed efficiently. The most suggestive and important information contained in the meshes and vector fields is preserved while less important areas are simplified in the visualization. Users can interactively control the level of detail by adjusting a range of clustering distance measure parameters. We describe two data structures to accelerate the clustering process. We also introduce novel visualizations of clusters inspired by statistical methods. We apply our method to a series of synthetic and complex, real-world CFD meshes to demonstrate the clustering algorithm results.

In this paper, the significance of slip situations in the appearance of a porous medium and frictional heating on unsteady fluid flow through a porous medium has been explored. The numerical solutions of the differential equation representing fluid flow through a porous material, including slip effects, are presented. We have obtained a nonlinear ordinary differential equation using a similarity transformation. Under velocity and thermal slip conditions, the Maple packages were used to numerically solve the resulting set of nonlinear problems. Both the velocity and temperature increase when the Brinkman viscosity ratio parameter [Formula: see text] increases. The effects of the nondimensional parameters on the governing flow velocity and temperature are examined with graphical profiles. The implications of relevant parameters on dimensionless temperature, velocity, local Nusselt number and skin friction coefficient are shown and explained. For various flow quantities of interest, the fluctuation of parameters is investigated, and the results are given in the system of graphs and tables.

This paper studies the nonlinear interactions between vortex-induced vibration of a spring-supported circular cylinder and the unsteady fluid flow in a narrow channel. The analytical model consists of two-dimensional incompressible viscous flow in a narrow channel at low Reynolds number, and the spring-supported cylinder that can move perpendicular to the wall of the channel. The marker-and-cell (MAC) method is used to calculate numerically the simultaneous equations governing the interaction between the motion of the cylinder and the unsteady fluid flow. Furthermore the numerical results are confirmed by experiments presented herein.