Advances in computational power now enable domain scientists to address conceptual and parametric uncertainty by running simulations multiple times in order to sufficiently sample the uncertain input space. While this approach helps address conceptual and parametric uncertainties, the ensemble datasets produced by this technique present a special challenge to visualization researchers as the ensemble dataset records a distribution of possible values for each location in the domain. Contemporary visualization approaches that rely solely on summary statistics (e.g., mean and variance) cannot convey the detailed information encoded in ensemble distributions that are paramount to ensemble analysis; summary statistics provide no information about modality classification and modality persistence. To address this problem, we propose a novel technique that classifies high-variance locations based on the modality of the distribution of ensemble predictions. Additionally, we develop a set of confidence metrics to inform the end-user of the quality of fit between the distribution at a given location and its assigned class. Finally, for the special application of evaluating the stability of bimodal regions, we develop local and regional metrics.

Visualization and analysis techniques play a key role in the discovery of relevant features in ensemble data. Trends, in the form of persisting commonalities or differences in time-varying ensemble datasets, constitute one of the most expressive feature types in ensemble analysis. We develop a flow-graph representation as the core of a system designed for the visual analysis of trends in time-varying ensembles. In our interactive analysis framework, this graph is linked to a representation of ensemble parameter-space and the ensemble itself. This facilitates a detailed examination of trends and their correlations to properties of input-space. We demonstrate the utility of the proposed trends analysis framework in several benchmark data sets, highlighting its capability to support goal-driven design of time-varying simulations.

Time surfaces are a versatile tool to visualise advection and deformation in flow fields. Due to complex flow behaviours involving stretching, shearing, and folding, straightforward mesh-based representations of these surfaces can develop artefacts and degenerate quickly. Common counter-measures rely on refinement and adaptive insertion of new particles which lead to an unpredictable increase in memory requirements. We propose a novel time surface extraction technique that keeps the number of required flow particles constant, while providing a high level of fidelity and enabling straightforward load balancing. Our solution implements a 2D particle relaxation procedure that makes use of local surface metric tensors to model surface deformations. We combine this with an accurate bicubic surface representation to provide an artefact-free surface visualisation. We demonstrate and evaluate benefits of the proposed method with respect to surface accuracy and computational efficiency.

Particle tracing in time-varying flow fields is traditionally performed by numerical integration of the underlying vector field. This procedure can become computationally expensive, especially in scattered, particle-based flow fields, which complicate interpolation due to the lack of an explicit neighborhood structure. If such a particle-based flow field allows for the identification of consecutive particle positions, an alternative approach to particle tracing can be employed: we substitute repeated numerical integration of vector data by geometric interpolation in the highly dynamic particle system as defined by the particle-based simulation. To allow for efficient and accurate location and interpolation of changing particle neighborhoods, we develop a modified k-d tree representation that is capable of creating a dynamic partitioning of even highly compressible data sets with strongly varying particle densities. With this representation we are able to efficiently perform pathline computation by identifying, tracking, and updating an enclosing, dynamic particle neighborhood as particles move overtime. We investigate and evaluate the complexity, accuracy, and robustness of this interpolation-based alternative approach to trajectory generation in compressible and incompressible particle systems generated by simulation techniques such as Smoothed Particle Hydrodynamics (SPH).

Effective display and visual analysis of complex 3D data is a challenging task. Occlusions, overlaps, and projective distortions-as frequently caused by typical 3D rendering techniques-can be major obstacles to unambiguous and robust data analysis. Slicing planes are a ubiquitous tool to resolve several of these issues. They act as simple clipping geometry to provide clear cut-away views of the data. We propose to enhance the visualization and analysis process by providing methods for automatic placement of such slicing planes based on local optimization of gradient vector flow. The final obtained slicing planes maximize the total amount of information displayed with respect to a pre-specified importance function. We demonstrate how such automated slicing plane placement is able to support and enrich 3D data visualization and analysis in multiple scenarios, such as volume or surface rendering, and evaluate its performance in several benchmark data sets.

Numerical ensemble forecasting is a powerful tool that drives many risk analysis efforts and decision making tasks. These ensembles are composed of individual simulations that each uniquely model a possible outcome for a common event of interest: e.g., the direction and force of a hurricane, or the path of travel and mortality rate of a pandemic. This paper presents a new visual strategy to help quantify and characterize a numerical ensemble's predictive uncertainty: i.e., the ability for ensemble constituents to accurately and consistently predict an event of interest based on ground truth observations. Our strategy employs a Bayesian framework to first construct a statistical aggregate from the ensemble. We extend the information obtained from the aggregate with a visualization strategy that characterizes predictive uncertainty at two levels: at a global level, which assesses the ensemble as a whole, as well as a local level, which examines each of the ensemble's constituents. Through this approach, modelers are able to better assess the predictive strengths and weaknesses of the ensemble as a whole, as well as individual models. We apply our method to two datasets to demonstrate its broad applicability.

Sets of simulation runs based on parameter and model variation, so-called ensembles, are increasingly used to model physical behaviors whose parameter space is too large or complex to be explored automatically. Visualization plays a key role in conveying important properties in ensembles, such as the degree to which members of the ensemble agree or disagree in their behavior. For ensembles of time-varying vector fields, there are numerous challenges for providing an expressive comparative visualization, among which is the requirement to relate the effect of individual flow divergence to joint transport characteristics of the ensemble. Yet, techniques developed for scalar ensembles are of little use in this context, as the notion of transport induced by a vector field cannot be modeled using such tools. We develop a Lagrangian framework for the comparison of flow fields in an ensemble. Our techniques evaluate individual and joint transport variance and introduce a classification space that facilitates incorporation of these properties into a common ensemble visualization. Variances of Lagrangian neighborhoods are computed using pathline integration and Principal Components Analysis. This allows for an inclusion of uncertainty measurements into the visualization and analysis approach. Our results demonstrate the usefulness and expressiveness of the presented method on several practical examples.

Multifluid simulations often create volume fraction data, representing fluid volumes per region or cell of a fluid data set. Accurate and visually realistic extraction of fluid boundaries is a challenging and essential task for efficient analysis of multifluid data. In this work, we present a new material interface reconstruction method for such volume fraction data. Within each cell of the data set, our method utilizes a gradient field approximation based on trilinearly blended Coons-patches to generate a volume fraction function, representing the change in volume fractions over the cells. A continuously varying isovalue field is applied to this function to produce a smooth interface that preserves the given volume fractions well. Further, the method allows user-controlled balance between volume accuracy and physical plausibility of the interface. The method works on two- and three-dimensional Cartesian grids, and handles multiple materials. Calculations are performed locally and utilize only the one-ring of cells surrounding a given cell, allowing visualizations of the material interfaces to be easily generated on a GPU or in a large-scale distributed parallel environment. Our results demonstrate the robustness, accuracy, and flexibility of the developed algorithms.

Characterizing the interplay between the vortices and forces acting on a wind turbine's blades in a qualitative and quantitative way holds the potential for significantly improving large wind turbine design. This paper introduces an integrated pipeline for highly effective wind and force field analysis and visualization. We extract vortices induced by a turbine's rotation in a wind field, and characterize vortices in conjunction with numerically simulated forces on the blade surfaces as these vortices strike another turbine's blades downstream. The scientifically relevant issue to be studied is the relationship between the extracted, approximate locations on the blades where vortices strike the blades and the forces that exist in those locations. This integrated approach is used to detect and analyze turbulent flow that causes local impact on the wind turbine blade structure. The results that we present are based on analyzing the wind and force field data sets generated by numerical simulations, and allow domain scientists to relate vortex-blade interactions with power output loss in turbines and turbine life expectancy. Our methods have the potential to improve turbine design to save costs related to turbine operation and maintenance.

Material interfaces and free surfaces are a topic of increasing interest in the field of computational fluid dynamics. In parts, reconstructed interfaces from such multi-fluid simulations behave like classic integral surfaces as known in the visualization community, while other regions of the surface undergo topological changes or behave orthogonally to what is expected by the underlying flow field. Thus, the analysis of the flow field in connection with material interface shape and topology is a challenging task. We develop a technique that facilitates visualization and analysis of such complex material interface behavior over time. For this matter, we track a surface parametrization of time-varying material interfaces and identify locations of interaction between material interfaces and fluid particles. Splatting and surface visualization techniques produce an intuitive representation of the derived interface stability. Our results demonstrate, how the interaction of the flow field with the material interface can be highlighted by appropriate extraction and visualization techniques and how the developed techniques can aid analysis of mixing and material interface consistency.

Integral flow surfaces constitute a widely used flow visualization tool due to their capability to convey important flow information such as fluid transport, mixing, and domain segmentation. Current flow surface rendering techniques limit their expressiveness, however, by focusing virtually exclusively on displacement visualization, visually neglecting the more complex notion of deformation such as shearing and stretching that is central to the field of continuum mechanics. To incorporate this information into the flow surface visualization and analysis process, we derive a metric tensor field that encodes local surface deformations as induced by the velocity gradient of the underlying flow field. We demonstrate how properties of the resulting metric tensor field are capable of enhancing present surface visualization and generation methods and develop novel surface querying, sampling, and visualization techniques. The provided results show how this step towards unifying classic flow visualization and more advanced concepts from continuum mechanics enables more detailed and improved flow analysis.

Crease surfaces describe extremal structures of 3D scalar fields. We present a new region-growing-based approach to the meshless extraction of adaptive nonmanifold valley and ridge surfaces that overcomes limitations of previous approaches by decoupling point seeding and triangulation of the surface. Our method is capable of extracting valley surface skeletons as connected minimum structures. As our algorithm is inherently mesh-free and curvature adaptive, it is suitable for surface construction in fields with an arbitrary neighborhood structure. As an application for insightful visualization with valley surfaces, we choose a low frequency acoustics simulation. We use our valley surface construction approach to visualize the resulting complex-valued scalar pressure field for arbitrary frequencies to identify regions of sound cancellation. This provides an expressive visualization of the topology of wave node and antinode structures in simulated acoustics.

A fundamental characteristic of fluid flow is that it causes mixing: introduce a dye into a flow, and it will disperse. Mixing can be used as a method to visualize and characterize flow. Because mixing is a process that occurs over time, it is a 4D problem that presents a challenge for computation, visualization, and analysis. Motivated by a mixing problem in geophysics, we introduce a combination of methods to analyze, transform, and finally visualize mixing in simulations of convection in a self-gravitating 3D spherical shell representing convection in the Earth's mantle. Geophysicists use tools such as the finite element model CitcomS to simulate convection, and introduce massless, passive tracers to model mixing. The output of geophysical flow simulation is hard to analyze for domain experts because of overall data size and complexity. In addition, information overload and occlusion are problems when visualizing a whole-earth model. To address the large size of the data, we rearrange the simulation data using intelligent indexing for fast file access and efficient caching. To address information overload and interpret mixing, we compute tracer concentration statistics, which are used to characterize mixing in mantle convection models. Our visualization uses a specially tailored version of Direct Volume Rendering. The most important adjustment is the use of constant opacity. Because of this special area of application, i. e. the rendering of a spherical shell, many computations for volume rendering can be optimized. These optimizations are essential to a smooth animation of the time-dependent simulation data. Our results show how our system can be used to quickly assess the simulation output and test hypotheses regarding Earth's mantle convection. The integrated processing pipeline helps geoscientists to focus on their main task of analyzing mantle homogenization.

Abstract The evolution of strain and development of material anisotropy in models of the Earth’s mantle flow convey important information about how to interpret the geometric relationship between observation of seismic anisotropy and the actual mantle flow field. By combining feature extraction techniques such as path line integration and tensor accumulation, we compute time‐varying strain vector fields that build the foundation for a number of feature extraction and visualization techniques. The proposed field segmentation, clustering, histograms and multi‐volume visualization techniques facilitate an intuitive understanding of three‐dimensional strain in such flow fields, overcoming limitations of previous methods such as 2‐D line plots and slicing. We present applications of our approach to an artificial time varying flow data set and a real world example of stationary flow in a subduction zone and discuss the challenges of processing these geophysical data sets as well as the insights gained.

Abstract This paper presents a novel method for the extraction and visualization of volume deformations in grid‐less point based flow simulations. Our primary goals are the segmentation of different paths through a mixing device and the visualization of ellipsoidal particle deformations. The main challenges are the numerically efficient processing of deformation tensors and the robust integration of stream‐ and streaklines at boundaries of the dataset such that closed segments are obtained. Our results show two‐ and three‐dimensional particle deformations as well as the segmentation of volumes in stationary fields and areas in time‐dependent datasets taking consistent paths through a mixing device.