Stony Brook AMS - Downloadable Preprints - 2005

Submitted to Phys. of Fluids
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SUNYSB-AMS-05-02	A Simple Package for Front Tracking	J. Du, B. Fix, J. Glimm, X. Jia, X. Li, Y. Li and L. Wu

We describe a general purpose software package for the geometry and dynamics of an interface. This package has been extracted from the FronTier code developed by the authors and colleagues, and is now available for general use. We compare accuracy and performance with a publically distributed version of the level set code. The interfaces consist of curves and points in 2D and surfaces, curves, and points in 3D, i.e. a general non-manifold geometry. Support for topological bifurcations and remeshing is provided, as well as standard geometrical constructions such as normal vectors, and curvature. The algorithm to resolve 3D bifurcations, Local Grid Based tracking (LGB) is new, and accordingly is described here in detail. It combines the robustness of grid based tracking with the accuracy of grid free tracking, and thus is a significant improvement to both of these algorithms. The package is written in C and C++, and it supports parallelism via MPI calls. In addition to mathematically motivated test problems, we illustrate performance in two applications which require a contact angle model, and for this purpose we also describe in detail a new contact angle propagation algorithm.

Submitted to Journal of Computational Physics
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SUNYSB-AMS-05-03	An Enhanced Front Tracking Method for the Computation of Discontinuous Structures in Fluid Dynamics	J. Glimm, X. Li, Y. Li, Z. Xu

The front tracking method is a high resolution method to study continuum mechanics with discontinuous interfaces. In this paper we discuss three important new developments for this method. The first development deals with the robust and high quality computation of dynamically moving front. We introduced a locally grid-based method which uses Lagrangian propagation and redistribution, but applies Eulerian reconstruction for the bifurcation of topology. This method maintains the high quality of the surface mesh and confines geometrical diffusion only to the regions where topological bifurcations are needed. Secondly, we have made important changes to the coupling of the finite difference interior solver and the front propagation. Global conservation is achieved by using the dynamic flux in the finite difference stencil near the interface. The third enhancement is to add the Colella-Burger adaptive mesh refinement method to the \FronTier code. This is accomplished by merging the \FronTier code with the \Overture code (Livermore) through the use of a common data model called the TSTT interface. We will demonstrate these features through application of the front tracking method to the computation of fluid interface instabilities.

Submitted to Proceeding of WCCM6
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SUNYSB-AMS-05-04	3D Image-Based Characterization of Fluid Displacement in a Berea Core	M. Prodanovic, W.B. Lindquist, and R.S. Seright

Improved network flow models require the incorporation of increasingly accurate geometrical characterization of the microscale pore structure as well as greater information on fluid-fluid interaction (interfaces) at pore scales. We report on three dimensional (3D) pore scale medium characterization, absolute permeability computations for throat structures, and pore scale residual fluid distribution in a Berea core. X-ray computed microtomography combined with X-ray attenuating dopants is used to obtain 3D images of the pore network and to resolve phase distributions in the pore space. We present results on pore characterization, including distributions for pore volume, pore surface area, throat surface area, and principal direction diameters for pores and throats. Lattice Boltzmann computations are used to predict absolute permeabilities for individual throats reconstructed from the images. We present results on oil and water distribution in the pore space at residual conditions. We also consider the effects on residual fluid distribution due to the injection and gelation of a water-based gel. In extensive studies of Berea cores it has been observed that introducing water-based gels in the displacement process reduces permeability to water more than to oil. Our results provide supporting evidence for the involvement of gel compaction (dehydration) and oil trapping, while discounting gel blockage in throats, as mechanisms contributing to this effect.

Submitted to Advances in Water Resources
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SUNYSB-AMS-05-05	LES Simulations of Turbulent Combustion in a Type Ia Supernovae	S. Dutta, J. Glimm, Y. Zhang

We propose a 2D axisymmetric model of a type Ia supernova explosion, based on a front tracking sharp flame model. The calculation is free from adjustable turbulent transport parameters, and in this sense it is in the spirit of Large Eddy Simulation (LES) turbulence simulations. Since the mixing is dominated by the largest eddies, we resolve these and not the smaller ones. We believe this method results in a tolerable error, which, in any case understates the success of the explosion. We report successful explosions. Both the 2D and the LES nature of the model greatly simplify parameter identification. The 2D model allows multiple simulations and an exploration of unknown parameters, while the LES model removes parameters from the simulation.

Submitted to Astrophysical Journal
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SUNYSB-AMS-05-06	Tracked Flame Simulation for Type Ia Supernova	Y. Zhang, J. Glimm, S. Dutta

In this paper, we present a numerical model for a Type Ia supernova explosion. Our method is based on explicit tracking of the flame front which is critically important to the accurate modeling of turbulent thermonuclear combustion.

To appear in Proceeding of Third MIT Conference, 2005.
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SUNYSB-AMS-05-07	Jet Simulation in a Diesel Engine	J. Glimm, M. Kim, X. Li, R. Samulyak, Z. Xu

In this paper, we report a numerical study of the jet breakup and spray formation in a diesel engine by the Front Tracking method. We model mixed vapor-liquid region through a heterogeneous model with dynamic vapor bubble insertion. On the liquid/vapor interface, a phase transition problem is solved numerically.

To appear in Proceeding of Third MIT Conference, 2005.
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SUNYSB-AMS-05-08	Atomization of a High Speed Jet	Zhiliang Xu, Myoungnyoun Kim, Wonho Oh, James Glimm, Roman Samulyak, Xiaolin Li, and Constantine Tzanos

A numerical study of atomization, \ie breakup of a high speed jet and spray formation, is presented using the Front Tracking method in 2D. The high speed flow in the nozzle gives rise to cavitation, \ie a mixed liquid-vapor region. To represent the state of the mixed phase, two different equation of state (EOS) models, a homogenized model and a discrete vapor bubble model, were used. In the homogenized model, the vapor-liquid mixture is treated as a single pseudofluid. In the discrete vapor bubble model, the mixed vapor-liquid mixture is modeled as a system of pure phase domains (vapor and liquid) separated by free interfaces. The major conclusion is that the jet breakup and spray characteristics depend strongly on the choice of EOS model, with only the discrete vapor bubble model producing breakup and plausible agreement with experimental data.

Submitted to Physics of Fluids
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SUNYSB-AMS-05-09	Mathematical Erosion as a Measure for Osteoporosis: Quantifying Topological Change	W.B. Lindquist, S. Chung, J. Pinezich, E. Gorin, and Y.-X. Qin

The evaluation of topological changes in the trabecular bone region provides insight into how trabecular bone protects itself against the effects of osteoporotic erosion and may provide essentials for fracture risk assessment at an early time point. Based on digital images obtained using micro computed tomography ($\mu$CT), a mathematical erosion model has been developed that enables the analysis of the relationship between virtual bone loss generated by (mathematical) erosion and the bone's structural alteration during progressive bone loss. The results demonstrate that erosion induced stresses are relieved through the preferential production of holes over breaks in the trabeculae. Trabecular bone appears constructed so that such preferential relief is able to continue down to extremely eroded forms of the structure. Further, the topological analysis indicates that trabecular structure is better protected against isotropic rather than unidirectional erosive action.

Submitted to J. BioMechanics
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SUNYSB-AMS-05-10	A Conservative Front Tracking Method	Jinjie Liu, James Glimm, and Xiaolin Li

We propose a fully conservative Front Tracking algorithm for systems of nonlinear conservation laws. The algorithm can be applied uniformly to one, two and three dimensional front tracking method. We report implementation of this algorithm and the tests of fully conservative simulations for all conserved variables.

Submitted to Proceedings of HYP2004
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SUNYSB-AMS-05-11	The Influence of Surface Tension on Turbulent Mixing Rates of Immiscible Fluids	Erwin George, James Glimm, Xiaolin Li, Yuanhua Li, and Xinfeng Liu

New simulations compare Rayleigh-Taylor mixing rates for ideal fluids and for real fluids with experimental values for surface tension. The simulated real fluid mixing rates agree with those measured experimentally within 5%. Comparison to theoretical predictions relating the mixing rate, the bubble width and the bubble height fluctuations based on bubble merger models shows similar agreement with experiment. The ideal fluid mixing rate is some 50% larger, providing an example of the sensitivity of the mixing rate to physical scale breaking interfacial phenomena; we also observe sensitivity to numerical scale breaking artifacts.

Submitted to Phys. Rev. Lett.
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SUNYSB-AMS-05-12	The Geometry of Primary Drainage	W.B. Lindquist

We show that arc menisci configuration under primary drainage in capillary tube cross sections and, by extension, in throats in the void structure of rock and soil, can be understood in terms of the computational geometry theory of medial axis analysis. The solution for arc meniscus configuration is developed for cross sections of arbitrary, simply connected polygonal shape at both entry- and over-pressure values during primary drainage for arbitrary values of wetting angle. Using this solution technique, we have obtained highly accurate solutions of entry pressure arc meniscus radius for over 21,500 throats obtained from analysis of computed tomography images in a suite of 4 Fontainebleau core samples ranging from 7.5% to 22% porosity. We show that the ratio A/P, of throat area to throat perimeter, is an excellent predictor of entry pressure meniscus radius (and hence entry pressure) for primary drainage for real pores, while inscribed radius and area equivalent radius over-predict entry pressure meniscusradius by factors of 1.5 to 3, and are consequently poor predictors.

Submitted to J. Colloid Interface Sci.
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SUNYSB-AMS-05-13	Porous Structure and Fluid Partitioning in Polyethylene Cores from 3D X-ray Microtomographic Imaging	M. Prodanovic, W.B. Lindquist, and R.S. Seright

Using oil-wet polyethylene core models, we present the development of robust throat finding techniques for the extraction, from X-ray microtomographic images, of a pore network description of porous media having porosity up to 50%. Measurements of volume, surface area, shape factor, and principle diameters are extracted for pores and area, shape factor and principle diameters for throats. We present results on the partitioning of wetting and non-wetting phase in the pore space at fixed volume increments of the injected fluid during a complete cycle of drainage and imbibition. We compare these results with fixed fractional flow injection, where wetting and non-wetting phase are simultaneously injected at fixed volume ratio. Finally we demonstrate the ability to differentiate three fluid phases (oil, water, air) in the pore space.

Submitted to J. Colloid Interface Sci.
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SUNYSB-AMS-05-14	A TSTT Integrated FronTier Code and Its Applications in Computational Fluid Physics	Brian Fix, James Glimm, Xiaolin Li, Yuanhua Li, Xinfeng Liu, Roman Samulyak and Zhiliang Xu

We introduce the FronTier-Lite software package and its adaptation to the TSTT geometry and and mesh entity data interface. This package is extracted from the original front tracking code for general scientific and engineering applications. The package contains a static interface library and a dynamic front propagation library. It can be used in research of different scientific problems. We demonstrate the applications of FronTier in the simulations of fuel injection jet, the fusion pellet injection and fluid mixing problems.

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SUNYSB-AMS-05-15	Computed Microtomography Studies of Fluid Partitioning in Drainage and Imbibition Before and After Gel Placement: Disproportionate Permeability Reduction	R.S. Seright, M. Prodanovic, and W.B. Lindquist

X-ray computed microtomography (XMT) was used to establish why pore-filling Cr(III)-acetate-HPAM gels reduced permeability to water much more than to oil. Our results suggest that permeability to water was reduced to low values because water must flow through gel itself, whereas oil pressing on the gel in Berea sandstone or porous polyethylene forced pathways by dehydration - leading to relatively high permeability to oil. In very permeable sand packs, data from other researchers supports ripping or extrusion mechanisms for creating oil pathways.

Our XMT studies provide interesting insights into imbibition and drainage processes in water-wet and oil-wet porous media even before gel placement. Many of our observations were consistent with conventional wisdom. However some were unexpected. Residual wetting phase (water) saturations in Berea were surprisingly low valued in small pores. We attribute this to surface roughness due to clay coating on Berea's pore walls which allowed efficient water drainage from small pores during oil injection.

To appear in the Society of Petroleum Engineers Journal
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SUNYSB-AMS-05-16	Uncertainty Quantification for Chaotic Computational Fluid Dynamics	Y. Yu, M. Zhao, T. Lee, N. Pestieau, W. Bo, James Glimm, J. W. Grove

We seek error models for simulations that model chaotic flow. Stable statistics for the solution and for the error are obtained after suitable averaging procedures.

Submitted to J. Comp. Phys.
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SUNYSB-AMS-05-17	Turbulent Mixing with Physical Mass Diffusion	Xinfeng Liu, Erwin George, Wurigen Bo, James Glimm

Simulated mixing rates of Rayleigh-Taylor instability for miscible fluids with physical mass diffusion are shown to agree with experiment; for immiscible fluids with physical values of surface tension the numerical data lies in the center of the experimental values. The simulations are based on an improved front tracking algorithm to control numerical surface tension and on improved physical modeling to allow physical values of mass diffusion or surface tension. Compressibility, after correction for variable density effects, has also been shown to have a strong influence on mixing rates. In summary, we find significant dependence of the mixing rates on scale breaking phenomena. We introduce tools to analyze the bubble merger process and confirm that bubble interactions, as in a bubble merger model, drive the mixing growth rate.

Submitted to Phy. Rev. E.
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SUNYSB-AMS-05-18	Recent Progress in the Stochastic Analysis of Turbulent Mixing	W. Bo, B. Cheng, J. Du, B. Fix, E George, J. Glimm, J. W. Grove, X. Jia, H. Jin, H. Lee, Y. Li, X. Li, X. Liu, D. H. Sharp, L. Wu and Y. Yu

We outline a program for the study of turbulent mixing of compressible fluids. We emphasize recent progress and steps still to be taken.

Submitted to Contemporary Mathematics.
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SUNYSB-AMS-05-19	Compressible Two-Pressure Two-Phase Flow Models	H. Jin, J. Glimm and D. H. Sharp

A central problem for compressible two-pressure two-phase flow models is closure, or the proper definition of averages of nonlinear terms. We propose here new closures for the velocity and momentum equations and discuss their validation.

Submitted to Phys. Lett. A
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SUNYSB-AMS-05-20	Neuroadaptive changes of Dendritic Spines in Nucleus Accumbens after Chronic Alcohol Drinking in Alcohol-Preferring Rats	F.C. Zhou, B. Anthony, K. Dunn, P. Deng, Z. Xu and W.B. Lindquist

Alcohol is known to affect glutamate (GLU) transmission. However, how chronic alcohol affects the synaptic structure mediating GLU transmission in the brain reward center is a key and unknown question pertinent to alcohol addiction. Repeated alcohol exposure in a subject with familial alcoholic history often leads to alcohol addiction. Current study adopts alcohol-preferring (P) rats which are known to develop high drinking levels without force or stress induction. P rats were treated, with 24-hour access of bottle choice of alcohol and water for 14 weeks (C-Alc group), with same access for the first 6 weeks followed by two repeated deprivation every other two weeks (RD-Alc group), or with water throughout 14 weeks (Water group). The medium spiny neurons (MSNs) of these animals were analyzed for dendritic structure in the key brain reward region nucleus accumbens (NAc) with two-photon microscopy and for N-methyl- D-aspartate (NMDA) receptor proteins. Chronic alcohol causes dysmorphology - thickened, beaded, and disoriented dendrites reminiscent reactive astrocytes - in subpopulation of MSNs. Furthermore, the density of dendritic spines was found differentially lower in the NAc of RD-Alc and C-Alc groups as compared with those of the Water groups. In contrast, large-sized spines and two-headed spines were increased in the RD-Alc group. The NMDA receptor subunit NR1 proteins, as analyzed with western blot, were upregulated in C-Alc, but not in RD-Alc. The upregulated NR1 however are predominantly a splice variance without exon 21 (C1 cassette) which is required for membrane-bound trafficking or anchoring into spine synaptic site. These maladaptations may also contribute to the transformation of spine head. Since spines are the presumable reception unit of the neurons and the head of spines are the primary site of GLU reception, the changes in density and head-size of spines and corresponding NMDA receptors demonstrated a micro-rewiring and plastic change. The current study demonstrated for the first time that chronic alcohol exposure causes plastic changes in dendrites as well as their spines in the key reward brain region in the animals that have a genetic background leading to alcohol addiction.

Submitted to J. Neurosci.
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Submitted to Computational Fluid and Solid Mechanics 2005
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