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At least 307 records · Page 17

Experimental validation of deterministic Acuros XB algorithm for IMRT and VMAT dose calculations with the Radiological Physics Center's head and neck phantom

Purpose: The purpose of this study was to verify the dosimetric performance of Acuros XB (AXB), a grid-based Boltzmann solver, in intensity-modulated radiation therapy (IMRT) and volumetric-modulated arc therapy (VMAT). Methods: The Radiological Physics Center (RPC) head and neck (H and N) phantom was used for all calculations and measurements in this study. Clinically equivalent IMRT and VMAT plans were created on the RPC H and N phantom in the Eclipse treatment planning system (version 10.0) by using RPC dose prescription specifications. The dose distributions were calculated with two different algorithms, AXB 11.0.03 and anisotropic analytical algorithm (AAA) 10.0.24. Two dose report modes of AXB were recorded: dose-to-medium in medium (D{sub m,m}) and dose-to-water in medium (D{sub w,m}). Each treatment plan was delivered to the RPC phantom three times for reproducibility by using a Varian Clinac iX linear accelerator. Absolute point dose and planar dose were measured with thermoluminescent dosimeters (TLDs) and GafChromic registered EBT2 film, respectively. Profile comparison and 2D gamma analysis were used to quantify the agreement between the film measurements and the calculated dose distributions from both AXB and AAA. The computation times for AAA and AXB were also evaluated. Results: Good agreement was observed between measured doses and those calculated with AAA or AXB. Both AAA and AXB calculated doses within 5% of TLD measurements in both the IMRT and VMAT plans. Results of AXB{sub Dm,m} (0.1% to 3.6%) were slightly better than AAA (0.2% to 4.6%) or AXB{sub Dw,m} (0.3% to 5.1%). The gamma analysis for both AAA and AXB met the RPC 7%/4 mm criteria (over 90% passed), whereas AXB{sub Dm,m} met 5%/3 mm criteria in most cases. AAA was 2 to 3 times faster than AXB for IMRT, whereas AXB was 4-6 times faster than AAA for VMAT. Conclusions: AXB was found to be satisfactorily accurate when compared to measurements in the RPC H and N phantom. Compared with AAA, AXB results were equal to or better than those obtained with film measurements for IMRT and VMAT plans. The AXB{sub Dm,m} reporting mode was found to be closer to TLD and film measurements than was the AXB{sub Dw,m} mode. AXB calculation time was found to be significantly shorter (x 4) than AAA for VMAT.

61 RADIATION PROTECTION AND DOSIMETRY↗

Building a Practical Natural Laminar Flow Design Capability

A preliminary natural laminar flow (NLF) design method that has been developed and applied to supersonic and transonic wings with moderate-to-high leading-edge sweeps at flight Reynolds numbers is further extended and evaluated in this paper. The modular design approach uses a knowledge-based design module linked with different flow solvers and boundary layer stability analysis methods to provide a multifidelity capability for NLF analysis and design. An assessment of the effects of different options for stability analysis is included using pressures and geometry from an NLF wing designed for the Common Research Model (CRM). Several extensions to the design module are described, including multiple new approaches to design for controlling attachment line contamination and transition. Finally, a modification to the NLF design algorithm that allows independent control of Tollmien-Schlichting (TS) and cross flow (CF) modes is proposed. A preliminary evaluation of the TS-only option applied to the design of an NLF nacelle for the CRM is performed that includes the use of a low-fidelity stability analysis directly in the design module.

Campbell, Richard L.↗

Exploring the Langtry-Menter Transition Model for High Speed Applications Using FUN3D

A series of Reynolds-averaged Navier-Stokes (RANS) simulations were performed using the FUN3D flow solver to explore the capabilities of the Langtry-Menter Shear-Stress Transport (LM-SST) transition model for predicting transition for aircraft inlet applications. Two geometries were simulated: a zero-pressure-gradient flat plate and an axisymmetric cone exposed to hypersonic flow. In addition to the transition-sensitized LM-SST model investigations, simulations were run with the one-equation Spalart-Allmaras (SA) and the two-equation Menter Shear-Stress Transport (SST-V) RANS models in fully turbulent mode to identify the natural RANS model transition behavior as a function of Mach number when executed in fully turbulent mode. The flat plate simulations showed that (1) the transition model was able to predict rapid transition at a freestream Mach number of 0.2, which is expected but (2) the predicted transition location moved downstream as the freestream Mach number was increased for the simulations that used the SST-V turbulence model. The latter is significant as it is usually assumed that one- and two-equation turbulence models will produce fully turbulent flow very near the boundary layer origin. The flat plate simulation freestream Mach number trend was confirmed with simulations using the Wind-US code, which also saw a similar trend when employing the SA turbulence model. For the axisymmetric cone simulations, the transition location was highly sensitive to the inflow turbulence levels. This is significant as the prediction of the transition location is crucial when trying to predict inlet performance, especially for hypersonic vehicle applications. It was also noted that the predicted transition location for the cone when using the SST-V turbulence model agreed well with the predicted transition location from the equivalent zero-pressure-gradient flat plate case.

Transition Model↗

Pedestal particle balance studies in JET-ILW H-mode plasmas

JET-ILW type I ELMy H-modes at 2.5 MA/2.8 T with constant NBI heating (23 MW) and gas fuelling rate were performed, utilising edge localised mode (ELM) pacing by vertical kicks and plasma shaping (triangularity, δ) as tools to disentangle the effects of ELMs, inter-ELM transport and edge stability on the pedestal particle balance. In agreement with previous studies, the pedestal confinement improves with increasing δ, mostly due to a significant increase in pedestal density while the ELM frequency ($f_{\mathrm{ELM}}$) is decreased. Improved pedestal confinement with increasing δ was observed even when the pedestal MHD stability was degraded artificially by vertical kicks, implying that increased triangularity may favourably affect the inter-ELM pedestal recovery. The workflow developed to quantify the pedestal particle balance uses high time-resolution profile reflectometry to characterise the inter-ELM evolution of the plasma particle content ($\mathrm{d} N/\mathrm{d}t$), the NEO drift-kinetic solver to evaluate the neoclassical fluxes and interpretative EDGE2D-EIRENE simulations to estimate the edge particle source. The edge particle source is then constrained by deuterium Balmer-α line intensity measurements in the main chamber, which are, however, strongly affected by reflections from the metal walls. The reflections are accounted for by the CHERAB code taking the divertor emission (the brightest light source in the torus) distribution from imaging spectroscopy measurements as input. Our analysis shows that in the second half of the ELM cycle, the volume-integrated particle source is larger than $\mathrm{d} N/\mathrm{d}t$, indicating that transport plays a key role in the inter-ELM pedestal recovery.

fuelling↗

Parallel variable-band Choleski solvers for computational structural analysis applications on vector multiprocessor supercomputers

A Choleski method used to solve linear systems of equations that arise in large scale structural analyses is described. The method uses a novel variable-band storage scheme and is structured to exploit fast local memory caches while minimizing data access delays between main memory and vector registers. Several parallel implementations of this method are described for the CRAY-2 and CRAY Y-MP computers demonstrating the use of microtasking and autotasking directives. A portable parallel language, FORCE, is also used for two different parallel implementations, demonstrating the use of CRAY macrotasking. Results are presented comparing the matrix factorization times for three representative structural analysis problems from runs made in both dedicated and multi-user modes on both the CRAY-2 and CRAY Y-MP computers. CPU and wall clock timings are given for the various parallel methods and are compared to single processor timings of the same algorithm. Computation rates over 1 GIGAFLOP (1 billion floating point operations per second) on a four processor CRAY-2 and over 2 GIGAFLOPS on an eight processor CRAY Y-MP are demonstrated as measured by wall clock time in a dedicated environment. Reduced wall clock times for the parallel methods relative to the single processor implementation of the same Choleski algorithm are also demonstrated for runs made in multi-user mode.

Poole, E. L.↗

Benchmarking core turbulence and transport predictions for an inductive compact tokamak reactor plasma

Motivated by the need for accurate, timely, and efficient calculations of plasma transport, predictions of plasma turbulence properties made using different TGLF saturation rules are benchmarked against corresponding predictions from linear and nonlinear gyrokinetic CGYRO simulations. This benchmarking is carried out using parameters taken from an inductive burning plasma scenario in a hypothetical compact high-field (R maj = 4 m, B T = 8 T) tokamak, lying in a much different regime of parameter space than either the TGLF calibration regime or current-day experiments. The core turbulent transport in this scenario is predicted to be dominated by ion temperature gradient (ITG) turbulence. In general, the ITG critical gradients predicted by various TGLF saturation rules are quite close to the CGYRO predictions. Both codes predict similar linear ITG growth rates and frequency spectra, as well as their scaling with R/L T i = −Rd ln(T i )/dr. However, TGLF systematically predicts unstable trapped-electron modes (TEMs) above k y ρ s ≃ 0.5 not seen by CGYRO for the same parameters, due to TGLF predicting a lower threshold in R/L T e than CGYRO for TEM onset. It is shown that for this scenario, nonlinear CGYRO simulations predict stiffer ITG turbulence than the TGLF SAT0 and SAT1 saturation rules, with energy fluxes close in magnitude and scaling with R/L T i to what is predicted by the SAT2 saturation rule. Self-consistent core profiles calculated using nonlinear CGYRO flux predictions and the PORTALS transport solver are shown to agree fairly well with corresponding predictions made using the TGLF SAT2 model, including a similar level of density peaking.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Equilibrium reconstruction of DIII-D plasmas using predictive modeling of the pressure profile

New workflows have been developed for predictive modeling of magnetohydrodynamic (MHD) equilibrium in tokamak plasmas. The goal of this work is to predict the MHD equilibrium in tokamak discharges without having measurements of the kinetic profiles. The workflows include a cold start tool, which constructs all the profiles and power flows needed by transport codes; a Grad–Shafranov equilibrium solver; and various codes for the sources and sinks. For validation purposes, a database of DIII-D tokamak discharges has been constructed that is comprised of scans in the plasma current, toroidal magnetic field, and triangularity. Initial efforts focused on developing a workflow utilizing an empirically derived pressure model tuned to DIII-D discharges with monotonic safety factor profiles. This workflow shows good agreement with experimental kinetic equilibrium calculations, but is limited in that it is a single fluid (equal ion and electron temperatures) model and lacks H-mode pedestal predictions. The best agreement with the H-mode database is obtained using a theory-based workflow utilizing pressure profile predictions from a coupled TGLF turbulent transport and EPED pedestal models together with external magnetics and Motional Stark Effect (MSE) data to construct the equilibrium. Here, we obtain an average root mean square error of 5.1% in the safety factor profile when comparing the predicted and experimental kinetic equilibrium. We also find good agreement with the plasma stored energy, internal inductance, and pressure profiles. Including MSE data in the theory-based workflow results in noticeably improved agreement with the q-profiles in high triangularity discharges in comparison with the results obtained with magnetic data only. The predictive equilibrium workflow is expected to have wide applications in experimental planning, between-shot analysis, and reactor studies.

Kinsey, J. E. (ORCID:0000000193347473)↗

Divertor leg filaments in NSTX-U

This study presents the first observation of divertor localized turbulence in the NSTX-Upgrade spherical tokamak. Previous work in NSTX discharges described fluctuations on the divertor target due to blobs generated on the low field side midplane. In the region that shows disconnection from upstream turbulence (private flux region and proximity of the strike point), divertor-localized fluctuations are observed via imaging of C III and D-α emission in diverted L-mode discharges and are characterized in this paper. Field-aligned filaments connected to the divertor target plate are radially localized at the separatrix on the outer divertor leg and in the private flux region on the inner divertor leg. These are limited to the region below the X-point with fluctuation levels up to 10%–20%. The filaments have comparable poloidal and radial correlation lengths (10–100 ion gyroradii ρ i ) and parallel correlation lengths of several meters. Toroidal mode numbers are in the range of 10–30 and 2–10 for outer and inner leg filaments. The poloidal motion of outer leg filaments has the same direction and comparable magnitude to advection due to E x B drift calculated by the multi-fluid edge transport code UEDGE with inclusion of cross field drifts. Disconnection between inner and outer leg filaments as well as the absence of correlation with upstream turbulence support the hypothesis of X-point disconnection for divertor leg filaments. Simulations with the ArbiTER linear eigenvalue solver and a resistive-balooning model were performed with a simulation grid limited to the divertor legs. Instabilities localized to the bad curvature side of the divertor legs were observed, in qualitative agreement with the experiment.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

On the Measurements of Numerical Viscosity and Resistivity in Eulerian MHD Codes

We propose a simple ansatz for estimating the value of the numerical resistivity and the numerical viscosity of any Eulerian MHD code. We test this ansatz with the help of simulations of the propagation of (magneto)sonic waves, Alfvén waves, and the tearing mode (TM) instability using the MHD code Aenus. By comparing the simulation results with analytical solutions of the resistive-viscous MHD equations and an empirical ansatz for the growth rate of TMs, we measure the numerical viscosity and resistivity of Aenus. The comparison shows that the fast magnetosonic speed and wavelength are the characteristic velocity and length, respectively, of the aforementioned (relatively simple) systems. We also determine the dependence of the numerical viscosity and resistivity on the time integration method, the spatial reconstruction scheme and (to a lesser extent) the Riemann solver employed in the simulations. From the measured results, we infer the numerical resolution (as a function of the spatial reconstruction method) required to properly resolve the growth and saturation level of the magnetic field amplified by the magnetorotational instability in the post-collapsed core of massive stars. Our results show that it is most advantageous to resort to ultra-high-order methods (e.g., the ninth-order monotonicity-preserving method) to tackle this problem properly, in particular, in three-dimensional simulations.

79 ASTRONOMY AND ASTROPHYSICS↗

Combustor Operability and Performance Verification for HIFiRE Flight 2

As part of the Hypersonic International Flight Research Experimentation (HIFiRE) Direct-Connect Rig (HDCR) test and analysis activity, three-dimensional computational fluid dynamics (CFD) simulations were performed using two Reynolds-Averaged Navier Stokes solvers. Measurements obtained from ground testing in the NASA Langley Arc-Heated Scramjet Test Facility (AHSTF) were used to specify inflow conditions for the simulations and combustor data from four representative tests were used as benchmarks. Test cases at simulated flight enthalpies of Mach 5.84, 6.5, 7.5, and 8.0 were analyzed. Modeling parameters (e.g., turbulent Schmidt number and compressibility treatment) were tuned such that the CFD results closely matched the experimental results. The tuned modeling parameters were used to establish a standard practice in HIFiRE combustor analysis. Combustor performance and operating mode were examined and were found to meet or exceed the objectives of the HIFiRE Flight 2 experiment. In addition, the calibrated CFD tools were then applied to make predictions of combustor operation and performance for the flight configuration and to aid in understanding the impacts of ground and flight uncertainties on combustor operation.

Storch, Andrea M.↗

Spatiotemporal evolution of runaway electrons from synchrotron images in Alcator C-Mod

In the Alcator C-Mod tokamak, relativistic runaway electron (RE) generation can occur during the flattop current phase of low density, diverted plasma discharges. Due to the high toroidal magnetic field (B0 = 5.4 T), RE synchrotron radiation is measured by a wide-view camera in the visible wavelength range (~400-900 nm). In this paper, a statistical analysis of over one thousand camera images is performed to investigate the plasma conditions under which synchrotron emission is observed in C-Mod. In addition, the spatiotemporal evolution of REs during one particular discharge is explored in detail via a thorough analysis of the distortion-corrected synchrotron images. To accurately predict RE energies, the kinetic solver CODE [Landreman et al 2014 Comput. Phys. Commun. 185 847-855] is used to evolve the electron momentum-space distribution at six locations throughout the plasma: the magnetic axis and flux surfaces q = 1, 4/3, 3/2, 2, and 3. These results, along with the experimentally-measured magnetic topology and camera geometry, are input into the synthetic diagnostic SOFT [Hoppe et al 2018 Nucl. Fusion 58 026032] to simulate synchrotron emission and detection. Interesting spatial structure near the surface q = 2 is found to coincide with the onset of a locked mode and increased MHD activity. Furthermore, the RE density profile evolution is fit by comparing experimental to synthetic images, providing important insight into RE spatiotemporal dynamics.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Investigation of a Parabolic Iterative Solver for Three-dimensional Configurations

A parabolic iterative solution procedure is investigated that seeks to extend the parabolic approximation used within the internal propagation module of the duct noise propagation and radiation code CDUCT-LaRC. The governing convected Helmholtz equation is split into a set of coupled equations governing propagation in the positive and negative directions. The proposed method utilizes an iterative procedure to solve the coupled equations in an attempt to account for possible reflections from internal bifurcations, impedance discontinuities, and duct terminations. A geometry consistent with the NASA Langley Curved Duct Test Rig is considered and the effects of acoustic treatment and non-anechoic termination are included. Two numerical implementations are studied and preliminary results indicate that improved accuracy in predicted amplitude and phase can be obtained for modes at a cut-off ratio of 1.7. Further predictions for modes at a cut-off ratio of 1.1 show improvement in predicted phase at the expense of increased amplitude error. Possible methods of improvement are suggested based on analytic and numerical analysis. It is hoped that coupling the parabolic iterative approach with less efficient, high fidelity finite element approaches will ultimately provide the capability to perform efficient, higher fidelity acoustic calculations within complex 3-D geometries for impedance eduction and noise propagation and radiation predictions.

Nark, Douglas M.↗

Computational Study of Variable Fuel-Air Ratio and Hydrogen Doping in a Rotating Detonation Engine

Rotating detonation engines (RDEs) hold great promise as a technology for powering aviation engines. The pressure gain that results from continuously traversing detonation waves enables high theoretical performance compared to deflagration-based combustion. However, the harsh operating conditions inside an RDE restrict the availability of suitable experimental diagnostics to study these systems in detail and the range of spatial and temporal scales render numerical simulations of these systems difficult. In this study, we have combined adaptive mesh refinement and a robust shock-capturing approach to study RDE systems computationally using the compressible, reactive solver PeleC. Multi-species transport along with compressible Navier-Stokes equations are solved in the model along with finite-rate chemistry. Complex geometries are represented using an embedded boundary method with second-order spatial accuracy and the system is evolved in time using a second-order Runge-Kutta method. We present studies of a methane-air RDE system that is doped with varying levels of hydrogen. Our analysis focusses on how fuel mixture and doping levels effect the detonation flame structure and the generation of multiple wave modes.

ADVANCED PROPULSION SYSTEMS↗

Quantum-Inspired Bayesian Sampling for Uncertainty Quantification and Machine Learning (Final Technical Report)

With increasing simulation and measurement data, machine learning and artificial intelligence have been widely used in computational decision-making of complex engineering systems. The resulting tools, such as uncertainty quantification solvers, reinforcement learning, and physics-informed machine learning, have achieved great success in critical DOE tasks such as material discovery and design, energy system modeling and control, and numerical weather and climate prediction. A core topic in scientific machine learning and artificial intelligence is Bayesian inference: given an observed data set, people want to estimate the posterior distribution of a (possibly large) number of hidden parameters. Due to the flexibility and weak assumptions, Bayesian sampling has been the mainstream Bayesian inference solvers despite the rapid progress of approximate Bayesian inference. Classical Bayesian sampling methods such as Markov-chain Monte Carlo suffer from a low-acceptance rate due to the random walk nature, therefore state-of-the-art techniques use Hamiltonian Monte Carlo and its variants to efficiently draw posterior samples in a high dimension. The key idea of Hamiltonian Monte Carlo and its variants is to simulate the Hamiltonian dynamics of a classical particle with a fixed mass, and their performance significantly degrades when the posterior distribution is highly spiky or has multiple modes. Leveraging the idea of quantum physics, this project has investigated new theory, algorithms and applications of Bayesian inference (especially Bayesian sampling). The main results include: (1) novel quantum-inspired Bayesian sampling methods that can lead to better accuracy for challenging multi-modal or spiky distributions, (2) more scalable machine learning framework leveraging tensor-compressed Bayesian inference, and (3) Bayesian and sampling approaches for verifying the robustness of continuous and binary neural networks.

97 MATHEMATICS AND COMPUTING↗

Assessing Uncertainties in Boundary Layer Transition Predictions for HIFiRE-1 at Non-zero Angles of Attack

Boundary layer stability was analyzed for the HIFiRE-1 flight vehicle geometry for ground tests conducted at the CUBRC LENS I hypersonic shock test facility and the Langley Research Center (LaRC) 20- inch Mach 6 Tunnel. Boundary layer stability results were compared to transition onset location obtained from discrete heat transfer measurements from thin film gauges during the CUBRC test and spatially continuous heat transfer measurements from thermal phosphor paint data during the LaRC test. The focus of this analysis was on conditions at non-zero angles of attack as stability analysis has already been performed at zero degrees angle of attack. Also, the transition onset data obtained during flight testing was at nonzero angles of attack, so this analysis could be expanded in the future to include the results of the flight test data. Stability analysis was performed using the 2D parabolized stability software suite STABL (Stability and Transition Analysis for Hypersonic Boundary Layers) developed at the University of Minnesota and the mean flow solutions were computed using the DPLR finite volume Navier-Stokes computational fluid dynamics (CFD) solver. A center line slice of the 3D mean flow solution was used for the stability analysis to incorporate the angle of attack effects while still taking advantage of the 2D STABL software suite. The N-factors at transition onset and the value of Re(sub theta)/M(sub e), commonly used to predict boundary layer transition onset, were compared for all conditions analyzed. Ground test data was analyzed at Mach 7.2 and Mach 6.0 and angles of attack of 1deg, 3deg and 5deg. At these conditions, the flow was found to be second mode dominant for the HIFiRE-1 slender cone geometry. On the leeward side of the vehicle, a strong trend of transition onset location with angle of attack was observed as the boundary layer on the leeward side of the vehicle developed inflection points at streamwise positions on the vehicle that correlated to angle of attack. Inflection points are a strong instability mechanism that lead to rapid breakdown and transition to turbulence. The transition onset location on the windward side of the vehicle displayed no trend with angle of attack or freestream Reynolds number and transition was observed farther down the vehicle than observed on the leeward side of the vehicle. In analysis of both windward and leeward sides of the vehicle, use of the N factor methodology to develop trends to predict boundary layer transition onset showed improvements over the Re(sub theta)/M(sub e) empirical correlation methodology. Stronger correlations and less scatter in the data were observed when using the N factor method for these cases.

Marek, Lindsay C.↗

Coupled Fluid-Structure Interaction Analysis of Solid Rocket Motor with Flexible Inhibitors

Flexible inhibitors are generally used in solid rocket motors (SRMs) as a means to control the burning of propellant. Vortices generated by the flow of propellant around the flexible inhibitors have been identified as a driving source of instabilities that can lead to thrust oscillations in launch vehicles. Potential coupling between the SRM thrust oscillations and structural vibration modes is an important risk factor in launch vehicle design. As a means to predict and better understand these phenomena, a multidisciplinary simulation capability that couples the NASA production CFD code, Loci/CHEM, with CFDRC's structural finite element code, CoBi, has been developed. This capability is crucial to the development of NASA's new space launch system (SLS). This paper summarizes the efforts in applying the coupled software to demonstrate and investigate fluid-structure interaction (FSI) phenomena between pressure waves and flexible inhibitors inside reusable solid rocket motors (RSRMs). The features of the fluid and structural solvers are described in detail, and the coupling methodology and interfacial continuity requirements are then presented in a general Eulerian-Lagrangian framework. The simulations presented herein utilize production level CFD with hybrid RANS/LES turbulence modeling and grid resolution in excess of 80 million cells. The fluid domain in the SRM is discretized using a general mixed polyhedral unstructured mesh, while full 3D shell elements are utilized in the structural domain for the flexible inhibitors. Verifications against analytical solutions for a structural model under a steady uniform pressure condition and under dynamic modal analysis show excellent agreement in terms of displacement distribution and eigenmode frequencies. The preliminary coupled results indicate that due to acoustic coupling, the dynamics of one of the more flexible inhibitors shift from its first modal frequency to the first acoustic frequency of the solid rocket motor. This insight could have profound implications for SRM and flexible inhibitor designs for current and future launch vehicles including SLS.

Yang, H. Q.↗

Conceptual design of a quadrupole kicker and study of beam dynamics for generating echoes in IOTA

In this project we design dipole and quadrupole stripline kickers for echo generation in the IOTA ring. We developed a semi-analytic solver for dipole and quadrupole kickers with curved plates of innitesimal thickness, and independently validated it against a nite element software code (FEMM). The analytic series converges rapidly and is in agreement with FEMM within 5% everywhere except at the tips of the plates. We also consider nite thickness plates of dierent shapes (curved and parallel) and compare the central eld quality and characteristic impedance. We nd that in the dipole case, the parallel plates provide better eld quality than curved plates while in the quadrupole case, the dierence is not signicant. The characteristic impedance of relevant modes are computed. Matching the characteristic impedance to an external load is necessary to prevent unwanted re ection and ringing.

43 PARTICLE ACCELERATORS↗

A computationally efficient P 1 radiation model for modern combustion systems utilizing pre-conditioned conjugate gradient methods

The iterative convergence of the P 1 radiation model can be slow in optically thin scenarios when employing classical iterative methods. In order to remedy this shortcoming, an in-house P 1 radiation model was interfaced with high performance, scalable, linear solver libraries. Next, the accuracies of P 1 radiation model calculations was assessed by comparing its predictions against discrete ordinates (DO) model calculations for prototypical problems representative of modern combustion systems. Corresponding benchmark results were also included for comparison. Utilizing Pre-Conditioners (PC) to the Conjugate Gradients (CG) method, the convergence time of the P 1 radiation model reduced by a factor of 30 for modest problem sizes and a factor of 70 for larger sized problems when compared against classical Gauss Seidel sweeps. Additionally, PC provided 50% computational savings compared to employing CG in a standalone mode. The P 1 model calculation times were about 25–30% of the DO model calculation time. The time to solution also scaled linearly with an increase in problem size. The weighted sum of gray gases model employed in this study in conjunction with the P 1 model provided good agreement against benchmark data with L 2 error norms (defined relative to corresponding DO calculations) improving when isotropic intensities were prevalent.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗