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DOE OSTI2016

SU-F-T-656: Monte Carlo Study On Air Activation Around a Medical Electron Linac

Purpose: In high energy photon therapy, several radiation protection issues result from photonuclear reactions. The activation of air - directly by photonuclear reactions as well as indirectly by capture of photoneutrons generated inside the linac head - is a major point of concern for the medical staff. The purpose of this study was to estimate the annual effective dose to medical workers due to activated air around a medical high energy electron linac by means of Monte Carlo simulations. Methods: The treatment head of a Varian Clinac in 18 MV-X mode as well as the surrounding concrete bunker were modeled and the radiation transport was simulated using the Monte Carlo code FLUKA, starting from the primary electron striking the bremsstrahlung target. The activation yields in air from photo-disintegration of O-16 and N-14 nuclei as well as from neutron capture on Ar-40 nuclei were obtained from the simulations. The activation build-up, radioactive decay and air ventilation were studied using a mathematical model. The annual effective dose to workers was estimated by using published isotope specific conversion factors. Results: The oxygen and nitrogen activation yields were in contrast to the argon activation yield found to be field size dependent. The impact of the treatment room ventilation on the different air activation products was investigated and quantified. An estimate with very conservative assumptions gave an annual effective dose to workers of < 1 mSv/a. Conclusion: From the results of this study it can be concluded that the contribution of air activation to the radiation exposure to medical workers should be negligible in modern photon therapy, especially when it is compared to the dose due to prompt neutrons and the activation of heavy solid materials such as the jaws and the collimators inside the linac head.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2014

Brownian aggregation rate of colloid particles with several active sites

We theoretically analyze the aggregation kinetics of colloid particles with several active sites. Such particles (so-called “patchy particles”) are well known as chemically anisotropic reactants, but the corresponding rate constant of their aggregation has not yet been established in a convenient analytical form. Using kinematic approximation for the diffusion problem, we derived an analytical formula for the diffusion-controlled reaction rate constant between two colloid particles (or clusters) with several small active sites under the following assumptions: the relative translational motion is Brownian diffusion, and the isotropic stochastic reorientation of each particle is Markovian and arbitrarily correlated. This formula was shown to produce accurate results in comparison with more sophisticated approaches. Also, to account for the case of a low number of active sites per particle we used Monte Carlo stochastic algorithm based on Gillespie method. Simulations showed that such discrete model is required when this number is less than 10. Finally, we applied the developed approach to the simulation of immunoagglutination, assuming that the formed clusters have fractal structure.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2014

SU-D-BRD-06: Automated Population-Based Planning for Whole Brain Radiation Therapy

Purpose: Treatment planning for whole brain radiation treatment is technically a simple process but in practice it takes valuable clinical time of repetitive and tedious tasks. This report presents a method that automatically segments the relevant target and normal tissues and creates a treatment plan in only a few minutes after patient simulation. Methods: Segmentation is performed automatically through morphological operations on the soft tissue. The treatment plan is generated by searching a database of previous cases for patients with similar anatomy. In this search, each database case is ranked in terms of similarity using a customized metric designed for sensitivity by including only geometrical changes that affect the dose distribution. The database case with the best match is automatically modified to replace relevant patient info and isocenter position while maintaining original beam and MLC settings. Results: Fifteen patients were used to validate the method. In each of these cases the anatomy was accurately segmented to mean Dice coefficients of 0.970 ± 0.008 for the brain, 0.846 ± 0.009 for the eyes and 0.672 ± 0.111 for the lens as compared to clinical segmentations. Each case was then subsequently matched against a database of 70 validated treatment plans and the best matching plan (termed auto-planned), was compared retrospectively with the clinical plans in terms of brain coverage and maximum doses to critical structures. Maximum doses were reduced by a maximum of 20.809 Gy for the left eye (mean 3.533), by 13.352 (1.311) for the right eye, and by 27.471 (4.856), 25.218 (6.315) for the left and right lens. Time from simulation to auto-plan was 3-4 minutes. Conclusion: Automated database- based matching is an alternative to classical treatment planning that improves quality while providing a cost—effective solution to planning through modifying previous validated plans to match a current patient's anatomy.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2013

Pore-Scale Simulation of Intragranular Diffusion: Effects of Incomplete Mixing on Macroscopic Manifestations

Diffusive mass transfer into and out of intragranular micropores ("intragranular diffusion") plays an important role in the large-scale transport of some groundwater contaminants. We are interested in understanding the combined effect of pore-scale advection and intragranular diffusion on solute transport at the effective porous medium scale. To study this problem, we have developed a three-dimensional pore-scale model of fluid flow and solute transport that incorporates diffusion into and out of intragranular pore spaces. Our model is based on the Smoothed Particle Hydrodynamics (SPH) simulation method, which represents fluid and solid phases by a mesh-free particle discretization. In the pore spaces, fluid flow is simulated by discretizing the Navier-Stokes equations using the SPH approach. Solute transport is represented by advection, diffusion within the fluid phase, and diffusion between the fluid and solid phases. Our model is implemented on large-scale parallel computing hardware, allowing us to simulate millions of computational particles and represent fully three-dimensional systems of pores and grains with arbitrarily complex physical geometry. We have used this model system to perform numerical experiments using various model porous media systems, which allows us to draw comparisons between macroscopic measures computed from the pore-scale simulations (such as breakthrough curves) and those predicted by macroscopic formulations that assume complete mixing over the representative volume. In this paper we present results of 3D simulations of pore-scale flow and transport, including cases with and without intragranular diffusion, in two model porous media, one with randomly-packed uniform spherical grains and a second with randomly-packed spheres drawn from a binary grain size distribution. Breakthrough curves were computed from the 3D simulations at various transport distances. Comparable breakthrough curves were computed using 1D macroscopic models with parameters determined independently to the degree possible. Based on comparisons of the pore-scale and macroscopic model results, we draw two primary conclusions. First, non-Fickian behavior is persistent and ubiquitous at the scales considered, and most cases are better represented by a multi-rate mass transfer model even when there is no distinct secondary porosity (i.e., no intragranular diffusion). This suggests that diffusive mass transfer processes between preferential flow paths and relatively immobile zones within the primary porosity may have significant impact on transport, particular in low-concentration tails. Second, the application of mass transfer rate parameters based on an assumption of well-mixed concentrations at the pore-scale tend to overestimate the amount of mass transfer that occurs in heterogeneous pore geometries in which preferential flow leads to incomplete pore-scale lateral mixing.

Environmental Molecular Sciences Laboratory↗

DOE OSTI2016

Multi-scale diffuse interface modeling of multi-component two-phase flow with partial miscibility

In this paper, we introduce a diffuse interface model to simulate multi-component two-phase flow with partial miscibility based on a realistic equation of state (e.g. Peng–Robinson equation of state). Because of partial miscibility, thermodynamic relations are used to model not only interfacial properties but also bulk properties, including density, composition, pressure, and realistic viscosity. As far as we know, this effort is the first time to use diffuse interface modeling based on equation of state for modeling of multi-component two-phase flow with partial miscibility. In numerical simulation, the key issue is to resolve the high contrast of scales from the microscopic interface composition to macroscale bulk fluid motion since the interface has a nanoscale thickness only. To efficiently solve this challenging problem, we develop a multi-scale simulation method. At the microscopic scale, we deduce a reduced interfacial equation under reasonable assumptions, and then we propose a formulation of capillary pressure, which is consistent with macroscale flow equations. Moreover, we show that Young–Laplace equation is an approximation of this capillarity formulation, and this formulation is also consistent with the concept of Tolman length, which is a correction of Young–Laplace equation. At the macroscopical scale, the interfaces are treated as discontinuous surfaces separating two phases of fluids. Our approach differs from conventional sharp-interface two-phase flow model in that we use the capillary pressure directly instead of a combination of surface tension and Young–Laplace equation because capillarity can be calculated from our proposed capillarity formulation. A compatible condition is also derived for the pressure in flow equations. Furthermore, based on the proposed capillarity formulation, we design an efficient numerical method for directly computing the capillary pressure between two fluids composed of multiple components. Finally, numerical tests are carried out to verify the effectiveness of the proposed multi-scale method.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2015

Adaptive resolution simulation of polarizable supramolecular coarse-grained water models

Multiscale simulations methods, such as adaptive resolution scheme, are becoming increasingly popular due to their significant computational advantages with respect to conventional atomistic simulations. For these kind of simulations, it is essential to develop accurate multiscale water models that can be used to solvate biophysical systems of interest. Recently, a 4-to-1 mapping was used to couple the bundled-simple point charge water with the MARTINI model. Here, we extend the supramolecular mapping to coarse-grained models with explicit charges. In particular, the two tested models are the polarizable water and big multiple water models associated with the MARTINI force field. As corresponding coarse-grained representations consist of several interaction sites, we couple orientational degrees of freedom of the atomistic and coarse-grained representations via a harmonic energy penalty term. This additional energy term aligns the dipole moments of both representations. We test this coupling by studying the system under applied static external electric field. We show that our approach leads to the correct reproduction of the relevant structural and dynamical properties.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

A numerically exact description of ultrafast vibrational decoherence in vibration-coupled electron transfer

Broadband pump–probe spectroscopy has been widely used to measure vibrational decoherence associated with the reaction coordinate in photoinduced ultrafast vibration-coupled electron transfer (VCET) reactions. These experiments provide insight into the interplay of intramolecular coordinates along the reaction coordinate. However, a general theoretical foundation for analyzing, and even for explaining rigorously, these data is lacking. In this work, we study vibrational decoherence in a model VCET reaction using the nearly exact time-dependent density matrix renormalization group simulation method. We explore how analyzing the density matrix with quantum information measures can help elucidate the evolution of vibrational coherence in simulations of dynamics. We examine how vibrational coherence is affected by electron transfer on the timescale of approximately 100 femtoseconds. Our results suggest that electron transfer, in the nonadiabatic model, changes the vibrational equilibrium position abruptly—an example of a “quantum quench” event. This explains the concomitant vibrational decoherence. We find that abrupt vibrational decoherence can be mitigated by wavepacket motion occurring on the timescale of the electron transfer.

Science & Technology - Other Topics↗

DOE OSTI2026

Scattering Processes from Quantum Simulation Algorithms for Scalar Field Theories

We provide practical simulation methods for scalar field theories on a quantum computer that yield improved asymptotics as well as concrete gate estimates for the simulation and physical qubit estimates using the surface code. We achieve these improvements through two optimizations. First, we consider a finite volume approach for estimating the elements of the S-matrix. This approach is appropriate in general for 1+1D and for certain low-energy elastic collisions in higher dimensions. Second, we implement our approach using a series of different fault-tolerant simulation algorithms for Hamiltonians formulated both in the field occupation basis and field amplitude basis. Our algorithms are based on either second-order Trotterization or qubitization. The cost of Trotterization in occupation basis scales as O ( λ N 7 | Ω | 3 / ( M 5 / 2 ϵ 3 / 2 ) ) where λ is the coupling strength, N is the occupation cutoff, | Ω | is the volume of the spatial lattice, M is the mass of the particles and ϵ is the uncertainty in the energy calculation used for the S -matrix determination. Qubitization in the field basis scales as O ( | Ω | 2 ( k 2 Λ + k M 2 ) / ϵ ) , where k is the cutoff in the field and Λ is a scaled coupling constant. We find in both cases that the bounds suggest physically meaningful simulations can be performed using on the order of 4 × 10 6 physical qubits and 10 12 T -gates which corresponds to roughly one day on a superconducting quantum computer with surface code and a cycle time of 100 ns. This places the simulation of scalar field theory within striking distance of the gate counts for the best available chemistry simulation results.

Hardy, Andrew [Toronto U.] (ORCID:0000000235817382↗

DOE OSTI2015

Hydroforming of elliptical cavities

Activities of the past several years in developing the technique of forming seamless (weldless) cavity cells by hydroforming are summarized. An overview of the technique developed at DESY for the fabrication of single cells and multicells of the TESLA cavity shape is given and the major rf results are presented. The forming is performed by expanding a seamless tube with internal water pressure while simultaneously swaging it axially. Prior to the expansion the tube is necked at the iris area and at the ends. Tube radii and axial displacements are computer controlled during the forming process in accordance with results of finite element method simulations for necking and expansion using the experimentally obtained strain-stress relationship of tube material. In cooperation with industry different methods of niobium seamless tube production have been explored. The most appropriate and successful method is a combination of spinning or deep drawing with flow forming. Several single-cell niobium cavities of the 1.3 GHz TESLA shape were produced by hydroforming. They reached accelerating gradients E acc up to 35 MV/m after buffered chemical polishing (BCP) and up to 42 MV/m after electropolishing (EP). More recent work concentrated on fabrication and testing of multicell and nine-cell cavities. Several seamless two- and three-cell units were explored. Accelerating gradients E acc of 30–35 MV/m were measured after BCP and E acc up to 40 MV/m were reached after EP. Nine-cell niobium cavities combining three three-cell units were completed at the company E. Zanon. These cavities reached accelerating gradients of E acc = 30–35 MV/m. One cavity is successfully integrated in an XFEL cryomodule and is used in the operation of the FLASH linear accelerator at DESY. Additionally the fabrication of bimetallic single-cell and multicell NbCu cavities by hydroforming was successfully developed. Several NbCu clad single-cell and double-cell cavities of the TESLA shape have been fabricated. The clad seamless tubes were produced using hot bonding or explosive bonding and subsequent flow forming. The thicknesses of Nb and Cu layers in the tube wall are about 1 and 3 mm respectively. The rf performance of the best NbCu clad cavities is similar to that of bulk Nb cavities. The highest accelerating gradient achieved was 40 MV/m. The advantages and disadvantages of hydroformed cavities are discussed in this paper.

36 MATERIALS SCIENCE↗

DOE OSTI2014

SU-E-T-577: Commissioning of a Deterministic Algorithm for External Photon Beams

Purpose: We report commissioning results for a deterministic algorithm for external photon beam treatment planning. A deterministic algorithm solves the radiation transport equations directly using a finite difference method, thus improve the accuracy of dose calculation, particularly under heterogeneous conditions with results similar to that of Monte Carlo (MC) simulation. Methods: Commissioning data for photon energies 6 – 15 MV includes the percentage depth dose (PDD) measured at SSD = 90 cm and output ratio in water (Spc), both normalized to 10 cm depth, for field sizes between 2 and 40 cm and depths between 0 and 40 cm. Off-axis ratio (OAR) for the same set of field sizes was used at 5 depths (dmax, 5, 10, 20, 30 cm). The final model was compared with the commissioning data as well as additional benchmark data. The benchmark data includes dose per MU determined for 17 points for SSD between 80 and 110 cm, depth between 5 and 20 cm, and lateral offset of up to 16.5 cm. Relative comparisons were made in a heterogeneous phantom made of cork and solid water. Results: Compared to the commissioning beam data, the agreement are generally better than 2% with large errors (up to 13%) observed in the buildup regions of the FDD and penumbra regions of the OAR profiles. The overall mean standard deviation is 0.04% when all data are taken into account. Compared to the benchmark data, the agreements are generally better than 2%. Relative comparison in heterogeneous phantom is in general better than 4%. Conclusion: A commercial deterministic algorithm was commissioned for megavoltage photon beams. In a homogeneous medium, the agreement between the algorithm and measurement at the benchmark points is generally better than 2%. The dose accuracy for a deterministic algorithm is better than a convolution algorithm in heterogeneous medium.

07 ISOTOPE AND RADIATION SOURCES↗

DOE OSTI2018

Monte Carlo simulation of cylinders with short-range attractions

Cylindrical or rod-like particles are promising materials for the applications of fillers in nanocomposite materials and additives to control rheological properties of colloidal suspensions. Recent advances in particle synthesis allows for cylinders to be manufactured with short-ranged attractions to study the gelation as a function of packing fraction, aspect ratio and attraction strength. In order to aid in the analysis of small-angle scattering experiments of rod-like particles, computer simulation methods were used to model these particles with specialized Monte Carlo algorithms and tabular superquadric potentials. The attractive interaction between neighboring rods increases with the amount of locally-accessible surface area, thus leading to patchy-like interactions. We characterize the clustering and percolation of cylinders as the attractive interaction increases from the homogenous fluid at relatively low attraction strength, for a variety of aspect ratios and packing fractions. Comparisons with the experimental scattering results are also presented, which are in agreement.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2016

An Integrated Computational Materials Engineering Method for Woven Carbon Fiber Composites Preforming Process

An integrated computational materials engineering method is proposed in this paper for analyzing the design and preforming process of woven carbon fiber composites. The goal is to reduce the cost and time needed for the mass production of structural composites. It integrates the simulation methods from the micro-scale to the macro-scale to capture the behavior of the composite material in the preforming process. In this way, the time consuming and high cost physical experiments and prototypes in the development of the manufacturing process can be circumvented. This method contains three parts: the micro-scale representative volume element (RVE) simulation to characterize the material; the metamodeling algorithm to generate the constitutive equations; and the macro-scale preforming simulation to predict the behavior of the composite material during forming. The results show the potential of this approach as a guidance to the design of composite materials and its manufacturing process.

Composite, Preforming, Integrated Computational Ma↗

DOE OSTI2015

A testpart for interdisciplinary analyses in micro production engineering

In 2011, a round robin test was initiated within the group of CIRP Research Affiliates. The aim was to establish a platform for linking interdisciplinary research in order to share the expertise and experiences of participants all over the world. This paper introduces a testpart which has been designed to allow an analysis of different manufacturing technologies, simulation methods, machinery and metrology as well as process and production planning aspects. Current investigations are presented focusing on the machining and additive processes to produce the geometry, simulation approaches, machine analysis, and a comparison of measuring technologies. Challenges and limitations regarding the manufacturing and evaluation of the testpart features by the applied methods are discussed.

42 ENGINEERING↗

DOE OSTI2014

Brachytherapy structural shielding calculations using Monte Carlo generated, monoenergetic data

Purpose: To provide a method for calculating the transmission of any broad photon beam with a known energy spectrum in the range of 20–1090 keV, through concrete and lead, based on the superposition of corresponding monoenergetic data obtained from Monte Carlo simulation. Methods: MCNP5 was used to calculate broad photon beam transmission data through varying thickness of lead and concrete, for monoenergetic point sources of energy in the range pertinent to brachytherapy (20–1090 keV, in 10 keV intervals). The three parameter empirical model introduced byArcher et al. [“Diagnostic x-ray shielding design based on an empirical model of photon attenuation,” Health Phys. 44, 507–517 (1983)] was used to describe the transmission curve for each of the 216 energy-material combinations. These three parameters, and hence the transmission curve, for any polyenergetic spectrum can then be obtained by superposition along the lines of Kharrati et al. [“Monte Carlo simulation of x-ray buildup factors of lead and its applications in shielding of diagnostic x-ray facilities,” Med. Phys. 34, 1398–1404 (2007)]. A simple program, incorporating a graphical user interface, was developed to facilitate the superposition of monoenergetic data, the graphical and tabular display of broad photon beam transmission curves, and the calculation of material thickness required for a given transmission from these curves. Results: Polyenergetic broad photon beam transmission curves of this work, calculated from the superposition of monoenergetic data, are compared to corresponding results in the literature. A good agreement is observed with results in the literature obtained from Monte Carlo simulations for the photon spectra emitted from bare point sources of various radionuclides. Differences are observed with corresponding results in the literature for x-ray spectra at various tube potentials, mainly due to the different broad beam conditions or x-ray spectra assumed. Conclusions: The data of this work allow for the accurate calculation of structural shielding thickness, taking into account the spectral variation with shield thickness, and broad beam conditions, in a realistic geometry. The simplicity of calculations also obviates the need for the use of crude transmission data estimates such as the half and tenth value layer indices. Although this study was primarily designed for brachytherapy, results might also be useful for radiology and nuclear medicine facility design, provided broad beam conditions apply.

61 RADIATION PROTECTION AND DOSIMETRY↗

DOE OSTI2016

MO-FG-209-02: Development of a Virtual Breast Phantom From a Multi-Modality Perspective

This symposium will review recent advances in the simulation methods for evaluation of novel breast imaging systems – the subject of AAPM Task Group TG234. Our focus will be on the various approaches to development and validation of software anthropomorphic phantoms and their use in the statistical assessment of novel imaging systems using such phantoms along with computational models for the x-ray image formation process. Due to the dynamic development and complex design of modern medical imaging systems, the simulation of anatomical structures, image acquisition modalities, and the image perception and analysis offers substantial benefits of reduced cost, duration, and radiation exposure, as well as the known ground-truth and wide variability in simulated anatomies. For these reasons, Virtual Clinical Trials (VCTs) have been increasingly accepted as a viable tool for preclinical assessment of x-ray and other breast imaging methods. Activities of TG234 have encompassed the optimization of protocols for simulation studies, including phantom specifications, the simulated data representation, models of the imaging process, and statistical assessment of simulated images. The symposium will discuss the state-of-the-science of VCTs for novel breast imaging systems, emphasizing recent developments and future directions. Presentations will discuss virtual phantoms for intermodality breast imaging performance comparisons, extension of the breast anatomy simulation to the cellular level, optimized integration of the simulated imaging chain, and the novel directions in the observer models design. Learning Objectives: Review novel results in developing and applying virtual phantoms for inter-modality breast imaging performance comparisons; Discuss the efforts to extend the computer simulation of breast anatomy and pathology to the cellular level; Summarize the state of the science in optimized integration of modules in the simulated imaging chain; Compare novel directions in the design of observer models for task based validation of imaging systems. PB: Research funding support from the NIH, NSF, and Komen for the Cure; NIH funded collaboration with Barco, Inc. and Hologic, Inc.; Consultant to Delaware State Univ. and NCCPM, UK. AA: Employed at Barco Healthcare.; P. Bakic, NIH: (NIGMS P20 #GM103446, NCI R01 #CA154444); M. Das, NIH Research grants.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2016

MO-FG-209-05: Towards a Feature-Based Anthropomorphic Model Observer

60 APPLIED LIFE SCIENCES↗

DOE OSTI2016

Free energy landscape and molecular pathways of gas hydrate nucleation

Despite the significance of gas hydrates in diverse areas, a quantitative knowledge of hydrate formation at a molecular level is missing. The impediment to acquiring this understanding is primarily attributed to the stochastic nature and ultra-fine scales of nucleation events, posing a great challenge for both experiment and simulation to explore hydrate nucleation. Here we employ advanced molecular simulation methods, including forward flux sampling (FFS), p{sub B} histogram analysis, and backward flux sampling, to overcome the limit of direct molecular simulation for exploring both the free energy landscape and molecular pathways of hydrate nucleation. First we test the half-cage order parameter (H-COP) which we developed for driving FFS, through conducting the p{sub B} histogram analysis. Our results indeed show that H-COP describes well the reaction coordinates of hydrate nucleation. Through the verified order parameter, we then directly compute the free energy landscape for hydrate nucleation by combining both forward and backward flux sampling. The calculated stationary distribution density, which is obtained independently of nucleation theory, is found to fit well against the classical nucleation theory (CNT). Subsequent analysis of the obtained large ensemble of hydrate nucleation trajectories show that although on average, hydrate formation is facilitated by a two-step like mechanism involving a gradual transition from an amorphous to a crystalline structure, there also exist nucleation pathways where hydrate crystallizes directly, without going through the amorphous stage. The CNT-like free energy profile and the structural diversity suggest the existence of multiple active transition pathways for hydrate nucleation, and possibly also imply the near degeneracy in their free energy profiles among different pathways. Our results thus bring a new perspective to the long standing question of how hydrates crystallize.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS2001

Development of a Hybrid RANS/LES Method for Compressible Mixing Layer Simulations

A hybrid method has been developed for simulations of compressible turbulent mixing layers. Such mixing layers dominate the flows in exhaust systems of modem day aircraft and also those of hypersonic vehicles currently under development. The hybrid method uses a Reynolds-averaged Navier-Stokes (RANS) procedure to calculate wall bounded regions entering a mixing section, and a Large Eddy Simulation (LES) procedure to calculate the mixing dominated regions. A numerical technique was developed to enable the use of the hybrid RANS/LES method on stretched, non-Cartesian grids. The hybrid RANS/LES method is applied to a benchmark compressible mixing layer experiment. Preliminary two-dimensional calculations are used to investigate the effects of axial grid density and boundary conditions. Actual LES calculations, performed in three spatial directions, indicated an initial vortex shedding followed by rapid transition to turbulence, which is in agreement with experimental observations.

Georgiadis, Nicholas J.↗