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Numerical Modeling of Space Plasma Flows: ASTRONUM-2009

ASP Conference Series, Vol. 429, 2010

Nikolai V. Pogorelov, Edouard Audit, and Gary P. Zank, eds.

VA POR: Visual, Statistical, and Structural Analysis of

Astrophysical Flows

John Clyne

National Center for Atmospheric Research, Boulder, Colorado USA

Kenny Gruchalla

National Renewable Energy Laboratory, Golden, Colorado USA

Mark Rast

University of Colorado, Boulder, Colorado USA

Abstract. In this paper we discuss recent developments in the capabilities of

VAPOR: a desktop application that leverages today’s powerful CPUs and GPUs

to enable visualization and analysis of terascale data sets using only a commodity

PC or laptop. We review VA POR’s current capabilities, highlighting support

for Adaptive Mesh Reﬁnement(AMR) grids, and present new developments in

interactive feature-based visualization and statistical analysis.

1. Introduction

Interactive visualization and analysis of data from astrophysical ﬂow simulations

faces increasing challenges with theever increasi ng size of thosecalculations. The

mismatchbetween visualization/analysis and computational resources means

that some form of data reduction must beemployed to maintain interactivity in

the visualization/analysis process. To date VAPOR has addressed this challenge

via multiresolution acce ss and Cartesian-volume region-of-interest(ROI) extrac-

tion (Clyne & Rast 2005). We brieﬂy sumarize here key elements of the VAPOR

visual dataanalysis environment before discussingat some length VA POR’ssup-

port for Adapative Mesh Reﬁnement(AMR) grids and recent developments in

iterative feature based visualization and analysis. These developments extend

the region-of-interest conceptto volumes deﬁnedby the solutionproperties and

ﬁeld variablecorrelations,loosely termed structures or features.

2. VA POR

1

Inprevious work we have described indetail many of thecapabilities of the

VAPOR package (Clyne & Rast 2005; Clyneet al. 2007; Rast & Clyne 2008;

Mininni et al. 2008b). Three key components distinguish VA POR from other

advanced visualizationpackages thatthe authors are aware of:

1

VAPOR open source available at http://www.vapor .ucar.edu

323

324 Clyne, Gruchalla, and Rast

• a wavelet based multiresolutiondata model enables interactive data brows-

ingof high-resolution simulation outputs usingonly modest computing

resources (e.g., a conventional desktop or laptop)

• a feature setthat is targeted toward the specialized analysis needs of the

astrophysical and geophysical computational ﬂuiddynamics communities

• a closecoupling between VAPOR’s highly interactiveexploratoryvisual-

ization capabilities and ITT’s fourth-generation scientiﬁc data processing

language, IDL

2.1. Multiresolution

VAPOR utilizes a hierarchical data representation as a strategy toapproach the

challenges of interactively analyzing large-scale data volumes. The simulation

outputs are storedhierarchically, with each levelin that hierarchy providing

a coarsened approximation of the dataatthe preceding level. This approach

exploits the factthat manyvisualization and analysis operations can tolerate a

level of information loss by retrievingonly the level of ﬁdelity that is required

for thecurrent operations. For analysis operations that require access to the

dataat full resolution, this approach still allows the original data to be accessed

in their entirety, without loss of information.

The hierarchical multiresolution access is accomplished through a wavelet

decomposition and reconstruction scheme (Clyne 2003). The dataare stored as

hierarchy of successively coarser wavelet coeﬃcients, with each level representing

a halvingof the data resolution along each spatial axis, resulting in an eight-

fold reduction in the size of the data volume, and thecorresponding reduction

in required visualization and analysis resources. Storing the data hierarchy

as wavelet coeﬃcients avoids the penalty of keeping multiple data copies. A

three-dimensional Haar wavelet(Haar 1910) is currently being used for this

transformation. Thecomputational cost of the forward and inverse transforms

are negligiblecompared to those incurredby readingor writing the data, allowing

the reconstruction of the dataat factor-of-two resolutions with only minimal

overhead.

This hierarchical dataaccess scheme allows an investigator to control the

ﬁdelity of data in accordance with the available resources, the desired interac-

tivity, and the requirements of the analysis. This forms the basis for an iterative

analysis process, where the investigator can interactively browsecoarsened rep-

resentations of the dataacross the global spatiotemporal domain to identify fea-

tures of interest. Once identiﬁed, the analysis domain canbe restricted to these

features,increasing the level of data resolution that canbe handled interactively.

Oftenboth visualinspection and numerical analysis are fairly insensitive to con-

siderable data coarsening (Clyne & Rast 2005), providing substantial savings in

computational costs and input/output overhead during theearly exploratory

stages of investigation when interactivity is most crucial. Of course, subsequent

veriﬁcation of the analysis results canbe accomplished less interactively at full

resolution if necessary.

VAPOR 325

Figure 1. Tens of thousands of vortical structures (left) in a high-resolution

simulation of Taylor-Green forced turbulence (Mininni, Alexakis, & Pouquet

2008a). A vortical feature identiﬁed and extracted from a data volume using

high global values of vorticity and low absolute values offeature-local helicity

(right), shown with streamlines seeded in the velocity ﬁeld. These types of

non-Cartesian regions of interest canbe isolated asstructures and examined

both visually and quantitatively.

2.2. Targeted features

While VAPOR supports numerous general purpose visualization algorithms. It

also provides capabilities tailored towards astrophysical and geophysical CFD

needs. Oneexample, discussed indetail in Mininni et al. (2008b),is the integra-

tion and display of magnetic ﬁeld lines advectedby a velocity ﬁel d. Other spe-

cialized algorithms, not reported el sewhere,include methods for visually guided

placement of streamline and pathline seedpoints based on physical properties of

the ﬂow such as local ﬁeld maximaor minima. Interactive seeding is facilitated

by cutting planes at arbitrary orientations in the volume and interactive probing

of the data values.

A recent development(Gruchalla et al. 2009) has foc used onbroadening

theconcept of a ROI beyond Cartesian sub-volumes to thecoherent structures

by combining multivariate volume visualization techniques (Kniss, Kindlmann,

& Hansen 2002; Doleisch, Gasser, & Hauser 2003) with a connected c omponent

analysis (Suzuki, Horibia, & Sugie 2003). Structures canbe broadly and iter-

atively deﬁnedby multivariate transfer functions, and can thus represent local

regions of correlation or anticorrelationbetweenﬁeld variables as well as those

identiﬁedby more traditional thresholdingof a single measure. The algorithm

executes a connected component analysis of the volume, based onuser deﬁned

opacityvalues in the transfer function, to labelindividual structures. Structure

dependent histograms of the original or other derived variables can thenbe dis-

played, and structure statistics canbe used toguide further selection, deﬁnition,

and identiﬁcation in an iterative reﬁnement loop. For example, from the tens

of thousands of vortical structures in a recent simulation of Taylor-Green forced

turbulence (Mininni, Alexakis, & Pouquet 2008a)those regions withbothhigh

326 Clyne, Gruchalla, and Rast

vorticity and low helicity canbe readily identiﬁed and extracted (Figure 1) and

compared toother highlyvortical but more helical regions. Suchnon-Cartesian

ROI extraction can signiﬁcantly reduce data volumes, with thecoordinates of the

voxels contained in the structures readily output for use in subsequent analysis.

2.3. Coupling visualization with quantitative dataanalysis

VAPOR seamlessly interfaces with ITT’s fourth-generatio n language IDL, allow-

ing investigators to perform rigorous quantitative analyses guidedby VAPOR’s

intrinsic 2D and 3D visualization capabilities. The integration of IDL and VA-

POR is facilitatedby metadata exchange deﬁning the attributes and and resolu-

tion of the data. A library of data-access routines allows IDL to read and write

data in VA POR’s wavelet-encoded representation—an approach that is readily

generalizable toother analysis packages. In typical usage, the investigator will

maintain simultaneously active VAPOR and IDL sessions, visually identifying

ROIs with VAPOR and exporting them to IDL for further study. Interactivity

is maintained if the ROI issuﬃciently small or if the operation issuﬃciently

well-behaved over coarsened approximations of the data (Clyne & Rast 2005).

Quantities derived in the IDL session are importedback i nto theexisting VA-

POR session for continued visualinvestigation. Through the iteration of this

process,large-scale data sets canbe interactively explored, visualized, and ana-

lyzed withoutthe usual delays causedby reading, writing, and operatingon the

dataarrays in full.

The primary beneﬁt of coupling visual data investigation with anhigh-

level dataanalysis language is the ability to target expensivecalculations of

derived quantities to speciﬁc ROIs. The memory and computing requirement

for calculating such variables in advance, across theentire domain, can require

exorbitant resources, delayingor preventing further analysis. Moreover, the

computation of some analysis quantities requires prior knowledge of the solution.

This is particularly true if they are deﬁnedby ﬁeld values (e.g. regions of

maximum or minimummeasure) or correlations between the ﬂow variables. The

new interactive non-Cartesian-volume feature based ROI capabilities of VA POR

allow, viaamultivariate transfer function, precise deﬁnition of ROIs based on

solutionproperties, and can thus focus analysis onhighly reduced sub-volumes.

3. AMR

VAPOR supports a form of the block structured AMR grid that is most closely

describedby MacNeice et al. (2000),implemented in the PARAMESH pack-

age, and presently employedby the FLASH astrophysical thermonuclear ﬂash

code

2

. Thecomputational domain is coveredby a base level, regular, Cartesian

grid with uniform sampling. The base grid is partitioned into uniformly sized,

non-overlapping blocks: eachblock contains the same number of samples and

covers the same size physical space. Individual parent blocks may be reﬁnedby

subdividing them into eight chi ld octants. This reﬁnement may be performed

recursively creatingan octree hierarchy, with varying levels of reﬁnement. A

2

http://ﬂash.uchicago.edu/website/home/

VAPOR 327

Figure 2. A 3D plume simulation computed with the FLASH astrophysical

thermonuclear ﬂash code. With on-the-ﬂy resampling toauniform grid, the

full range of VAPOR capabilities are directly applicable to the AMR gridded

data.

maximum depth of 10 or 20 levels is not uncommon. All blocks in the hierarchy

contain the same number of uniformly distributed samples. VAPOR supports

a somewhat less restrictive AMR mess structure than that of PARAMESH, not

requiring that adjacent blocks diﬀer by no more than one level of reﬁnement.

Direct visualization of AMR grids is a complex task. Only recently have

practical algorithms been published for such routine visualization algorithms as

direct volume renderingor isosurface construction (Weber et al. 2001b,a). VA-

POR supports numerous fundamental visualization algorithms as well as novel

visualization methods not found in other packages. Toavoid the onerous task

of ge neralizi ngall of VA POR’s principal visualization methods to support both

regularrectilinear grids and a variety of AMR strategies, the approach taken

by VA POR is to resample AMR grids ontoauniformly sampled Cartesian grid.

The resampling is performed on the ﬂy, as needed, and atthe resolution selected

by the user. The user controlled sampling frequency matches a reﬁnement level

in the AMR grid, withblocks in the ROI possessingacoarser sampling than

the user speciﬁeddesired sampling reﬁned through interpolation, and blocks

of ﬁner AMR sampling coarsened. This treatment is analogous to the wavelet

based coarseningand reﬁning that underlies VAPOR operations on regularrec-

tilinear grids. Thecomputational cost of this regridding is fairly modest and is

ameliorated somewhat by VAPOR’s extensiveemployment of caching.

At presentthe only AMR ﬁle formatthat VAPOR’s interactive analysis tool,

”vaporgui”,is capable of reading is VAPOR’s own custom format. Pr eparing

an AMR data set for analysis with VAPOR requires ﬁrsttranslating the data

into this format. Command line utilities are provided for translation of FLASH

data setsstored i n the HDF5 ﬁle format

3

. Further, examplecodes are provided

that may becustomized for use with other AMR encodings.

3

http://www.hdfgroup.org

328 Clyne, Gruchalla, and Rast

4. Conclusion

VAPOR continues to evolve to meetthe visualization and analysis challenges

facing computational astrophysical and geophysical ﬂuiddynamicists as we near

petascalecomputecapabilities. The focus remains onprovidingaﬂexible and

useful tool for use in interactive analysis. Both adaptive mesh reﬁnement and

data volume reduction inpost-batch analysis will beessential to interactivity in

the petascaleenvironment, and eﬃcient algorithmic mergingof these remains

an ongoing challenge.

Acknowledgments. This work was funded inpart by the National Science

Foundation under grant ITR-0325934. The AMR plume data was providedby

Matthias Rempel, and that of Taylor-Green turbulence by Pablo Mininni.

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