Stony Brook AMS - Downloadable Preprints, 2003

A 3D image geometry analysis package was used to measure the vesicularity, specific surface area and interconnectivity of the vesicles. The results of the analyses showed that the bubbles have roughly spheroidal forms of different sizes. Vesicularity ranged from 45% for lavas to 80% for scoria. At least 90% of the vesicles are interconnected. Specific surface area was determined both by counting voxel faces and by use of 2-point correlation functions.

A series of measurements of the structure of a variety of porous materials has been made using synchrotron computed microtomography (SCMT). The work was carried out at the Brookhaven National Synchrotron Light Source (NSLS), the Argonne Advanced Photon Source (APS) and the European Synchrotron Radiation Facility (ESRF). The experiments at Brookhaven and Argonne were carried out on bending magnet beam lines using area detectors to obtain CT images based on determination of X-ray absorption coefficients. The work at the ESRF used an undulator beam line, a 13 KeV pencil X-ray beam of 2 um, and an energy dispersive X-ray detector to make tomographic sections of trace element distributions by X-ray fluorescence tomography. Most of the work was done with a pixel/voxel size ranging from 0.002 to 0.010 mm. We examined the structure of unconsolidated estuarine sediments, whose structure is relevant to transport of contaminants in rivers and estuaries. Fluorescent tomography with 2-3 um resolution was used to ascertain whether or not metals were concentrated on the surface or throughout the volume of a single sediment particle. Sandstone samples were investigated to obtain a set of values describing their microstructures that could be useful in fluid flow calculations relevant to petroleum recovery or transport of environmental contaminants. Measurements were also made on sandstone samples that had been subjected to high-pressure compression to investigate the relation between the microgeometry and the magnitude of the applied pressure. Finally, a Wood's metal-filled sample was scanned for demonstration of resolution enhancement and fluid flow studies.

Short Course Lecture, SIAM Conference on Computational Science and Engineering 2003, San Diego, CA, February, 2003.

ABSTRACT GOES HERE

ABSTRACT GOES HERE

Numerical simulations of a spherical shock refraction have been successfully conducted by a front tracking method. We demonstrate the efficiency of the front tracking algorithm by comparing the $L_1$-error of spherical simulations by tracked and untracked methods. We find that the tracked algorithm is about 64 (256) times faster than the corresponding method without tracking the interface for a 2d (3d) simulation.

We are concerned here with the analysis and partition of uncertainty into component pieces, for a model prediction problem for flow in porous media.

In this paper, we present a two fluid mixing model based on hyperbolic equations having complete state variables (velocity, pressure, temperature) for each fluid. The numerical algorithm is an extension of a front tracking method from microdynamics to macrodynamics. The numerical results are validated by comparison to the incompressible limit.

This paper follows our earlier works on axisymmetric flows in curved geometry where algorithms, theories, experiments, simulations, applications and validations were presented. Our purpose here is to quantitatively study the effectiveness and efficiency of explicit front tracking. A study is carried out by comparing the $L_1$-error for spherical shock refraction simulations with and without tracking. We show that front tracking is a fast algorithm in the sense that it can reduce the level of mesh refinement needed to achieve a specified error tolerance by a significant factor compared to corresponding methods without tracking. Thus front tracking can both substantially reduce the computational time as well as memory usage for simulations with contacts or material interfaces.

We seek error models for shock physics simulations that are robust and understandable. The purpose of this paper is to formulate and validate a composition law to estimate errors in the solutions of composite problems in terms of the errors from simpler ones. We illustrate this idea in a simple context.

We present an overview of computational science at Brookhaven National Laboratory (BNL), with selections from three areas: fluids, nanoscience, and biology. The work at BNL in each of these areas is itself very broad, and we select a few topics for presentation within each of them.

Front tracking has proved to be an accurate and efficient algorithm in the sense that tracking the interface can reduce the error significantly~\cite{DutGliGro03a,DutGliGro03b}. By applying this algorithm, we conduct numerical simulations of Richtmyer-Meshkov (RM) instabilities in spherical geometry for axisymmetric flow. We demonstrate scaling invariance with respect to shock Mach number for fluid mixing statistics, such as growth rate and volume fraction. Here the mixing is related to bulk transport rather than molecular mixing. Our results are validated by convergence under both mesh refinement and statistical ensemble averaging. We also show that the spherical geometry will converge to planar geometry when the number of modes of interface perturbation goes to infinity.

We propose statistical models. To represent errors in shock physics simulations we propose a composition law to estimate errors in the solutions of composite problems in terms of the errors from simpler ones as discussed in a previous paper \cite{GliGroKan03}. The purpose of this report is to further validate this idea by applying it to the full list of wave interactions introduced in \cite{GliGroKan03}.

Uncertainty quantification is essential in using numerical models for prediction. While many works focused on how the uncertainty of the inputs propagate to the outputs, the modeling errors of the numerical model were often overlooked. In our Bayesian framework, modeling errors play an essential role and were assessed through studying numerical solution errors. The main ideas and key concepts will be illustrated through an oil reservoir case study. In this study, inference on the input has to be made from the output. Bayesian analysis is adopted to handle this inverse problem, then combine it with the forward simulation for prediction. The solution error models were established based on the scale-up solutions and fine-grid solutions. As the central piece of our framework, the robustness of these error models is fundamental. In addition to the oil reservoir computer codes, we will also discuss the modelling of solution error of shock wave physics. Although the framework itself is simple, there is many statistical challenges which include optimal dimension of the error model, trade-off between sample size and the solution accuracy. These challenges are also discussed.

We discuss two-pressure two-phase flow models. A central problem in such models is closure or the proper definition of averages of nonlinear terms. Here we compare various proposed closures. We introduce physical constraints closures should satisfy to conserve the total energy and phase entropy and to satisfy boundary conditions at the edges of the mixing zones. We find one closure which satisfies these constraints. The integral identities for the closures are derived based on a mixing zone homogeneity assumption. An entropy inequality introduces a new constraint which relates the two mixing zone edge motions.

We describe the synthesis of automated neuron branching morphology and spine detection algorithms to provide multiscale three-dimensional morphological analysis of neurons. The resulting software is applied to the analysis of a high resolution (0.098 x 0.098 x 0.081 micron^3) image of an entire pyramidal neuron from layer III of the superior temporal cortex in rhesus macaque monkey. The approach provides a highly automated, complete morphologic analysis of the entire neuron; each dendritic branch segment is characterized by several parameters including branch order, length, and radius as a function of distance along the branch, as well as by the locations, lengths, shape classification (e.g. mushroom, stubby, thin), and density distribution of spines on the branch. Results for this automated analysis are compared to published results obtained by other computer assisted manual means.

We present a high resolution study of the void space geometry of vesiculated basalts (porosities in the range 60% to 80%) from three dimensional digitized images obtained by synchrotron X-ray tomography. The void space is composed of vesicles, the solidified remnants of expanding gas bubbles. Coalescence between bubbles complicates the identification of individual vesicles. Under the assumption that coalescence between two bubbles results in a local throat configuration between the two resulting vesicles, we present an algorithm to locate the "contact surfaces" which conceptually separate coalesced vesicles. With contact surfaces identified, individual vesicles are isolated and analysis of their geometry and connectivity can be investigated. We present results for the distributions of vesicle volume, contact surface area and vesicle coordination number (the number of neighbors with which a vesicle has coalesced). We find that distribution for contact surface area is log-normal; the distribution for coordination number is a power-law; and the distribution of vesicle volumes is at least bi-modal.

X-ray computed microtomography (XMT) was used to understand why a Cr(III)-acetate-HPAM gel reduced permeability to water 80-90 times more than that to oil in strongly water-wet Berea sandstone and in strongly oil-wet porous polyethylene. During oil flow after gel placement in Berea, a 55% (average) reduction in gel volume occurred in pores of all detected size ranges, thus leading to a relatively high permeability to oil. In porous polyethylene, reduction in gel volume occurred mainly in small pores. Because the first oil injection after gel placement did not reduce gel volume to a greater extent in large pores than in small pores, the reduction in gel volume was probably caused by gel dehydration rather than by gel ripping or extrusion.

The overall Sor in Berea jumped from 18.4% before gel placement to 51% after. The greater level of trapped oil greatly restricted water flow. Before gel placement, most residual non-wetting blobs were isolated within individual pores. In Berea at Sor after gel placement, the largest residual oil blob was 122 times larger than the largest oil blob at Sor before gel placement. This high degree of connectivity for the oil phase explains the relatively high permeability to oil after gel placement. This large blob may exist because gel affinity for water limited the formation of water films that were needed to break the large oil blob into small blobs.

In porous polyethylene, the overall Sor was significantly lower after gel placement than before gel placement (0.3% versus 17.0%). Thus, oil trapping could not explain the large disproportionate permeability reduction (Frrw/Frro = 89). Gel dehydration and rehydration provide a viable explanation. In particular, paths may open during oil injection by partial dehydration of the gel. During subsequent water injection, the paths could partially close when the gel rehydrates.

Available as MicroSoft Word