2010

J. Luitjens, J. Guilkey, T. Harman, B. Worthen, S.G. Parker.
**“Adaptive Computations in the Uintah Framework,”** In *Advanced Computational Infastructures for Parallel/Distributed Adapative Applications*, Ch. 1, Wiley Press, 2010.

J. Luitjens.
**“The Scalability of Parallel Adaptive Mesh Refinement Within Uintah,”** *School of Computing, University of Utah*, 2010.

Solutions to Partial Differential Equations (PDEs) are often computed by discretizing the domain into a collection of computational elements referred to as a mesh. This solution is an approximation with an error that decreases as the mesh spacing decreases. However, decreasing the mesh spacing also increases the computational requirements. Adaptive mesh refinement (AMR) attempts to reduce the error while limiting the increase in computational requirements by refining the mesh locally in regions of the domain that have large error while maintaining a coarse mesh in other portions of the domain. This approach often provides a solution that is as accurate as that obtained from a much larger fixed mesh simulation, thus saving on both computational time and memory. However, historically, these AMR operations often limit the overall scalability of the application.

Adapting the mesh at runtime necessitates scalable regridding and load balancing algorithms. This dissertation analyzes the performance bottlenecks for a widely used regridding algorithm and presents two new algorithms which exhibit ideal scalability. In addition, a scalable space-filling curve generation algorithm for dynamic load balancing is also presented. The performance of these algorithms is analyzed by determining their theoretical complexity, deriving performance models, and comparing the observed performance to those performance models. The models are then used to predict performance on larger numbers of processors. This analysis demonstrates the necessity of these algorithms at larger numbers of processors. This dissertation also investigates methods to more accurately predict workloads based on measurements taken at runtime. While the methods used are not new, the application of these methods to the load balancing process is. These methods are shown to be highly accurate and able to predict the workload within 3% error. By improving the accuracy of these estimations, the load imbalance of the simulation can be reduced, thereby increasing the overall performance.

Finally, the scalability of AMR simulations as a whole using these algorithms is tested within the Uintah computational framework. Scalability tests are performed using up to 98,304 processors and nearly ideal scalability is demonstrated.

Q. Meng, J. Luitjens, M. Berzins.
**“Dynamic Task Scheduling for Scalable Parallel AMR in the Uintah Framework,”** SCI Technical Report, No. UUSCI-2010-001, *SCI Institute, University of Utah*, 2010.

Q. Meng, J. Luitjens, M. Berzins.
**“Dynamic Task Scheduling for the Uintah Framework,”** In *Proceedings of the 3rd IEEE Workshop on Many-Task Computing on Grids and Supercomputers (MTAGS10)*, pp. 1--10. 2010.

DOI: 10.1109/MTAGS.2010.5699431

Uintah is a computational framework for fluid-structure interaction problems using a combination of the ICE fluid flow algorithm, adaptive mesh refinement (AMR) and MPM particle methods. Uintah uses domain decomposition with a task-graph approach for asynchronous communication and automatic message generation. The Uintah software has been used for a decade with its original task scheduler that ran computational tasks in a predefined static order. In order to improve the performance of Uintah for petascale architecture, a new dynamic task scheduler allowing better overlapping of the communication and computation is designed and evaluated in this study. The new scheduler supports asynchronous, out-of-order scheduling of computational tasks by putting them in a distributed directed acyclic graph (DAG) and by isolating task memory and keeping multiple copies of task variables in a data warehouse when necessary. A new runtime system has been implemented with a two-stage priority queuing architecture to improve the scheduling efficiency. The effectiveness of this new approach is shown through an analysis of the performance of the software on large scale fluid-structure examples.

J. Schmidt, M. Berzins.
**“Development of the Uintah Gateway for Fluid-Structure-Interaction Problems,”** In *Proceedings of the Teragrid 2010 Conference*, ACM, 2010.

DOI: 10.1145/1838574.1838591

P.C. Wallstedt, J.E. Guilkey.
**“A Weighted Least Squares Particle-In-Cell Method for Solid Mechanics,”** In *International Journal for Numerical Methods in Engineering*, Vol. 85, No. 13, pp. 1687--1704. April, 2010.

DOI: 10.1002/nme.3041

A novel meshfree method is proposed that incorporates features of the material point (MPM) and generalized interpolation material point (GIMP) methods and can be used within an existing MPM/GIMP implementation. Weighted least squares kernel functions are centered at stationary grid nodes and used to approximate field values and gradients. Integration is performed over cells of the background grid and material boundaries are approximated with an implicit surface. The proposed method avoids nearest-neighbor searches while significantly improving accuracy over MPM and GIMP. Implementation is discussed in detail and several example problems are solved, including one manufactured solution which allows measurement of dynamic, non-linear, large deformation performance. Advantages and disadvantages of the method are discussed.

**Keywords:** generalized interpolation material point method, meshfree, marching cubes, weighted least squares, implicit surface, MPM, GIMP, PIC

2009

J. Guilkey, T. Harman, J. Luitjens, J. Schmidt, J. Thornock, J.D. de St. Germain, S. Shankar, J. Peterson, C. Brownlee.
**“Uintah User Guide Version 1.1,”** SCI Technical Report, No. UUSCI-2009-007, *SCI Institute, University of Utah*, 2009.

T.L. Henriksen, G.J. Nathan, Z.T. Alwahabi, N. Qamar, T.A. Ring, E.G. Eddings.
**“Planar Measurements of Soot Volume Fraction and OH in a JP-8 Pool Fire,”** In *Combustion and Flame*, Vol. 156, No. 7, pp. 1480--1492. 2009.

DOI: 10.1016/j.combustflame.2009.03.002

The simultaneous measurement of soot volume fraction by laser induced incandescence (LII) and qualitative imaging of OH by laser induced fluorescence (LIF) was performed in a JP-8 pool fire contained in a 152 mm diameter pan. Line of sight extinction was used to calibrate the LII system in a laminar flame, and to provide an independent method of measuring average soot volume fraction in the turbulent flame. The presence of soot in the turbulent flame was found to be approximately 50% probable, resulting in high levels of optical extinction, which increased slightly through the flame from approximately 30% near the base, to approximately 50% at the tip. This high soot loading pushes both techniques toward their detection limit. Nevertheless, useful accuracy was obtained, with the LII measurement of apparent extinction in the turbulent flame being approximately 21% lower than a direct measurement, consistent with the influence of signal trapping. The axial and radial distributions of soot volume fraction are presented, along with PDFs of volume fraction, and new insight into the behavior of soot sheets in pool fires are sought from the simultaneous measurements of OH and LII.

**Keywords:** Incandescence, Fluorescence, Pool fire, JP-8

J.B. Hooper, D. Bedrov, G.D. Smith, B. Hanson, O. Borodin, D.M. Dattelbaum, E.M. Kober.
**“A molecular dynamics simulation study of the pressure-volume-temperature behavior of polymers under high pressure,”** In *Journal of Chemical Physics*, 2009.

DOI: 10.1063/1.3077868

Isothermal compression of poly (dimethylsiloxane), 1,4-poly(butadiene), and a model Estane® (in both pure form and a nitroplasticized composition similar to PBX-9501 binder) at pressures up to **100kbars** has been studied using atomistic molecular dynamics (MD) simulations. Comparison of predicted compression, bulk modulus, and ** U_{s--}u_{p}** behavior with experimental static and dynamic compression data available in the literature reveals good agreement between experiment and simulation, indicating that MD simulations utilizing simple quantum-chemistry-based potentials can be used to accurately predict the behavior of polymers at relatively high pressure. Despite their very different zero-pressure bulk moduli, the compression, modulus, and

L.K. Huynh, H.R. Zhang, S. Zhang, E.G. Eddings, A.F. Sarofim, M.E. Law, P.R. Westmoreland, T.N. Truong.
**“Kinetics of Enol Formation from Reaction of OH with Propene,”** In *Journal of Physical Chemistry*, Vol. 113, No. 13, pp. 3177--3185. 2009.

DOI: 10.1021/jp808050j

Kinetics of enol generation from propene has been predicted in an effort to understand the presence of enols in flames. A potential energy surface for reaction of OH with propene was computed by CCSD(T)/cc-pVDZ//B3LYP/cc-pVTZ calculations. Rate constants of different product channels and branching ratios were then calculated using the Master Equation formulation (*J. Phys. Chem. A 2006, 110*, 10528). Of the two enol products, ethenol is dominant over propenol, and its pathway is also the dominant pathway for the OH + propene addition reactions to form bimolecular products. In the temperature range considered, hydrogen abstraction dominated propene + OH consumption by a branching ratio of more than 90%. Calculated rate constants of enol formation were included in the Utah Surrogate Mechanism to model the enol profile in a cyclohexane premixed flame. The extended model shows consistency with experimental data and gives 5% contribution of ethenol formation from OH + propene reaction, the rest coming from ethene + OH.

J. Luitjens, M. Berzins.
**“Uintah: A Scalable Adaptive Framework for Emerging Petascale Platforms,”** SCI Technical Report, No. UUSCI-2009-002, *SCI Institute, University of Utah*, 2009.

J. Van Rij, T. Ameel, T. Harman.
**“An evaluation of secondary effects on microchannel frictional and convective heat transfer characteristics,”** In *International Journal of Heat and Mass Transfer*, Vol. 52, No. 11-12, pp. 2792--2801. 2009.

DOI: 10.1016/j.ijheatmasstransfer.2009.01.001

The frictional and convective heat transfer characteristics of rarified flows in rectangular microchannels, with either isoflux or isothermal boundary conditions, are evaluated subject to second-order slip boundary conditions, creep flow, viscous dissipation, and axial conduction effects. Numerical results are obtained using a continuum based, three-dimensional, compressible, unsteady computational fluid dynamics algorithm with first- and second-order slip velocity and temperature jump boundary conditions applied to the momentum and energy equations, respectively. The results, reported in the form of Poiseuille and Nusselt numbers, are found to be significant functions of aspect ratio, Knudsen number, slip model parameters, Brinkman number, and Peclet number.

**Keywords:** Rarified flow, Viscous dissipation, Axial conduction

J. Van Rij, T. Ameel, T. Harman.
**“The Effect of Viscous Dissipation and Rarefaction on Rectangular Microchannel Convective Heat Transfer,”** In *International Journal of Thermal Sciences*, Vol. 48, No. 2, pp. 271--281. February, 2009.

DOI: 10.1016/j.ijthermalsci.2008.07.010

The effect of viscous dissipation and rarefaction on rectangular microchannel convective heat transfer rates, as given by the Nusselt number, is numerically evaluated subject to constant wall heat flux (H2) and constant wall temperature (T) thermal boundary conditions. Numerical results are obtained using a continuum based, three-dimensional, compressible, unsteady computational fluid dynamics algorithm with slip velocity and temperature jump boundary conditions applied to the momentum and energy equations, respectively. For the limiting case of parallel plate channels, analytic solutions for the thermally and hydrodynamically fully developed momentum and energy equations are derived, subject to both first- and second-order slip velocity and temperature jump boundary conditions, from which analytic Nusselt number solutions are then obtained. Excellent agreement between the analytical and numerical results verifies the accuracy of the numerical algorithm, which is then employed to obtain three-dimensional rectangular channel and thermally/hydrodynamically developing Nusselt numbers. Nusselt number data are presented as functions of Knudsen number, Brinkman number, Peclet number, momentum and thermal accommodation coefficients, and aspect ratio. Rarefaction and viscous dissipation effects are shown to significantly affect the convective heat transfer rate in the slip flow regime.

**Keywords:** Microchannel, Nusselt number, Slip flow, Brinkman number, Viscous dissipation

M. Steffen.
**“Analysis-Guided Improvements of the Material Point Method,”** *School of Computing, University of Utah*, 2009.

The Material Point Method (MPM) has shown itself to be a powerful tool in the simulation of large deformation problems, especially those involving complex geometries and contact where typical finite element type methods frequently fail. While these large complex problems lead to some impressive simulations and solutions, there has been a lack of basic analysis characterizing the errors present in the method, even on the simplest of problems. However, like most methods which employ mixed Lagrangian (particle) and Eulerian strategies, analysis of the method is not straight forward. The lack of an analysis framework for MPM, as is found in finite element methods, makes it challenging to explain anomalies found in its employment and makes it difficult to propose methodology improvements with predictable outcomes. In this dissertation, we provide a formal analysis of the errors in MPM and use this analysis to direct proposed improvements. In particular, we will focus on how the lack of regularity in the grid functions used for representing the solution can hamper both spatial and temporal convergence of the method. We will show how the use of smoother basis functions, such as B-splines, can improve the accuracy of the method. An in-depth analysis of the current time stepping methods will help to explain behavior currently demonstrated numerically in the literature and will allow users of the method to understand the balance of spatial and temporal errors in MPM. Lastly, extrapolation techniques will be proposed to improve quadrature errors in the method.

L.T. Tran, J. Kim, M. Berzins.
**“Solving Time-Dependent PDEs using the Material Point Method, A Case Study from Gas Dynamics,”** In *International Journal for Numerical Methods in Fluids*, Vol. 62, No. 7, pp. 709--732. 2009.

H.R. Zhang, E.G. Eddings, A.F. Sarofim, C.K. Westbrook.
**“Fuel dependence of benzene pathways,”** In *Proceedings of the Combustion Institute*, Vol. 32, No. 1, pp. 377--385. 2009.

DOI: 10.1016/j.proci.2008.06.011

The relative importance of formation pathways for benzene, an important precursor to soot formation, was determined from the simulation of 22 premixed flames for a wide range of equivalence ratios (1.0–3.06), fuels (C_{1}–C_{12}), and pressures (20–760 torr). The maximum benzene concentrations in 15 out of these flames were well reproduced within 30% of the experimental data. Fuel structural properties were found to be critical for benzene production. Cyclohexanes and C_{3} and C_{4} fuels were found to be among the most productive in benzene formation; and long-chain normal paraffins produce the least amount of benzene. Other properties, such as equivalence ratio and combustion temperatures, were also found to be important in determining the amount of benzene produced in flames. Reaction pathways for benzene formation were examined critically in four premixed flames of structurally different fuels of acetylene, *n*-decane, butadiene, and cyclohexane. Reactions involving precursors, such as C_{3} and C_{4} species, were examined. Combination reactions of C_{3} species were identified to be the major benzene formation routes with the exception of the cyclohexane flame, in which benzene is formed exclusively from cascading fuel dehydrogenation via cyclohexene and cyclohexadiene intermediates. Acetylene addition makes a minor contribution to benzene formation, except in the butadiene flame where C_{4}H_{5} radicals are produced directly from the fuel, and in the n-decane flame where C_{4}H_{5} radicals are produced from large alkyl radical decomposition and H atom abstraction from the resulting large olefins.

2008

O. Borodin, G.D. Smith, T.D. Sewell, D. Bedrov.
**“Polarizable and Nonpolarizable Force Fields for Alkyl Nitrates,”** In *Journal of Physical Chemistry, B*, Vol. 112, No. 3, pp. 734--742. 2008.

DOI: 10.1021/jp076149f

Quantum-chemistry-based many-body polarizable and two-body nonpolarizable atomic force fields were developed for alkyl nitrate liquids and pentaerythritol tetranitrate (PETN) crystal. Bonding, bending, and torsional parameters, partial charges, and atomic polarizabilities for the polarizable force field were determined from gas-phase quantum chemistry calculations for alkyl nitrate oligomers and PETN performed at the MP2/aug-cc-pvDz level of theory. Partial charges for the nonpolarizable force field were determined by fitting the dipole moments and electrostatic potential to values for PETN molecules in the crystal phase obtained from molecular dynamics simulations using the polarizable force field. Molecular dynamics simulations of alkyl nitrate liquids and two polymorphs of PETN crystal demonstrate the ability of the quantum-chemistry-based force fields to accurately predict thermophysical and mechanical properties of these materials.

H. Davande, D. Bedrov, G.D. Smith.
**“Thermodynamic, Transport and Viscoelastic Properties of PBX-9501 Binder: A Molecular Dynamics Simulation Study,”** In *Journal of Energetic Materials*, Vol. 26, No. 2, pp. 115--138. 2008.

DOI: 10.1080/07370650701801937

Atomistic molecular dynamics simulations were performed on a low-molecular-weight nitroplasticized Estane® mixture representative of the binder used in PBX-9501. Pressure-volume-temperature (PVT) behavior over a wide range of pressures and temperatures above the order-disorder temperature (ODT) of Estane was determined and represented with the empirical Tait and Sun equations of state. The effect of temperature, pressure, and plasticization on transport properties of the mixture was also examined. A combination of molecular dynamics simulations and theoretical reptation models was used to predict the shear stress relaxation modulus G(t) of PBX-9501 binder at 473 K and 1 atm pressure. Data obtained from simulations of the model PBX-9501 binder presented here can be utilized to predict the temperature and pressure dependence of the shear stress relaxation modulus for temperatures above the ODT.

C. Gribble, C. Brownlee, S.G. Parker.
**“Practical Global Illumination for Interactive Particle Visualization,”** In *Computers and Graphics*, Vol. 32, No. 1, pp. 14--24. February, 2008.

DOI: 10.1016/j.cag.2007.11.001

Particle-based simulation methods are used to model a wide range of complex phenomena and to solve time-dependent problems of various scales. Effective visualizations of the resulting state will communicate subtle changes in the three-dimensional structure, spatial organization, and qualitative trends within a simulation as it evolves. We present two algorithms targeting upcoming, highly parallel multicore desktop systems to enable interactive navigation and exploration of large particle data sets with global illumination effects. Monte Carlo path tracing and texture mapping are used to capture computationally expensive illumination effects such as soft shadows and diffuse interreflection. The first approach is based on precomputation of luminance textures and removes expensive illumination calculations from the interactive rendering pipeline. The second approach is based on dynamic luminance texture generation and decouples interactive rendering from the computation of global illumination effects. These algorithms provide visual cues that enhance the ability to perform analysis and feature detection tasks while interrogating the data at interactive rates. We explore the performance of these algorithms and demonstrate their effectiveness using several large data sets.

**Keywords:** Interactive particle visualization, Global illumination, Ray tracing

T.L. Henriksen, T.A. Ring, E.G. Eddings, G.J. Nathan.
**“Puffing Frequency and Soot Extinction Correlation in JP-8 and Heptane Pool Fires,”** In *Combustion Science and Technology*, Vol. 180, No. 4, 2008.

DOI: 10.1080/00102200701845524

A new approach for characterizing puffing frequency was established by performing total extinction measurements on pool fires of JP-8 (Jet Propulsion Fuel 8) and heptane using a multiple beam extinction experiment. A maximum entropy method (MEM) was applied to extract a characteristic extinction frequency that was found to correlate well with puffing frequency. The measured extinction frequency for both flames was found to have some variation with height, though this is small. The amplitude of the frequency of the measured oscillations was found to be higher for JP-8 than for heptane, and became constant one diameter above the fuel pan for both flames. The variance of total extinction in the JP-8 and heptane pool fires was approximately 20% and 17%, respectively. Correlation statistics between the various extinguished beams reveal an increase in axi-symmetry of the instantaneous oscillations with height above the pool.