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At least 739 records · Page 41
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Large eddy simulation of a supersonic lifted hydrogen flame: Impacts of Lewis, turbulent Schmidt and Prandtl numbers

Parametric large eddy simulations (LES) of a supersonic lifted hydrogen flame are reported. The emphases are on two aspects: impacts of (1) Lewis number (Lei of the ith species) and (2) turbulent Schmidt and Prandtl numbers (⁠Sc t and Pr t ⁠) on supersonic turbulent flame and flow structures. Five cases are considered: species-specific Le i , Sc t = Sr t = 1.0 (C 0 ); unity Le i , Sc t = Pr t = 1.0 (C 1 ); species-specific Sc t = 0.5, Pr t = 1.0 (C 2 ); species-specific Le i , Sc t = 1.0, Pr t = 0.5 (C 3 ); and species-specific Le i , Sc t = Pr t = 0.5 (C 4 ). Numerical results of instantaneous and/or time-averaged species mole fractions, mixture fraction, heat release rate, flame base location, and mixed modes of premixed and diffusion combustion are compared between cases C 0 and C 1 . Differences in auto-ignition locations and strengths and flame structures and stabilization specify the impacts of Lewis number. They are triggered by different predictions of species mass and thermal diffusions at fuel-coflow and/or coflow-ambient air mixing layers. These differences are rationalized by a scale analysis of mass/thermal diffusion and convection for case C 0 , which suggests the relatively low but non-negligible former against the latter. Cases C 0 and C 2 –C 4 barely see differences in terms of instantaneous and/or time-averaged temperature, velocity, and mixed combustion modes except for further downstream areas where combustion occurs. Both Sc t and Pr t impose less significant influences than Lewis number, as sub-grid scale mass/thermal diffusion is subordinate to its resolved counterpart according to their scale analysis for case C 4 .

42 ENGINEERING↗
DOE OSTI2020

Grassy ELM regime at low pedestal collisionality in high-power tokamak plasma

Spontaneous mitigation of giant ELMs and appearance of grassy ELMs have been observed repeatedly at low pedestal collisionality (${\nu }_{\mathrm{e},\mathrm{p}\mathrm{e}\mathrm{d}}^{{\ast}}\sim 0.15$) in the high-power (P inj > 13 MW) hybrid scenario in DIII-D. Higher β p and higher q 95 appear to be beneficial to achieving the grassy ELM regime. The grassy ELM H-mode plasma shows high energy confinement performance (H 98y2 up to over 1.5) under the conditions of high neutral beam torque and high core rotation. The pedestal width appears to exceed the EPED1.0 model prediction by more than 50%. Pedestal stability analysis performed with the ELITE code indicates that the stability against low-n kink/peeling modes is improved with increased auxiliary heating power and the operational point in the grassy ELM regime is located near the ballooning boundary. The pedestal stability characteristics during the grassy ELM crashes have been investigated in comparison with the giant ELM crashes based on plasma profiles experimentally measured with high resolution and accuracy. It has been found that the underlying mechanism for the observed small-amplitude ELM crashes is mainly the expansion of the ballooning stability boundary induced by an initial radially localized collapse in the pedestal, which helps to stop the growth of instabilities and further collapse of the pedestal. The effect of electron density pedestal on mitigating edge localized instabilities has been analyzed by numerical simulation, suggesting that the electron density pedestal characterized by high n e,sep /n e,ped and low density gradient helps to stabilize peeling-ballooning modes because of a low pressure pedestal gradient and to lower the ballooning boundary mainly because of a low ion diamagnetic frequency in the pedestal region, thus triggering ballooning instabilities and producing the intrinsic grassy ELMs. Numerical simulation of the Chinese fusion engineering test reactor (CFETR) with the SOLPS code indicates that the separatrix density might be insensitive to the electron diffusivity in the pedestal region and increase with the power flowing from the core region to the edge region. Furthermore, pedestal stability analysis suggests that the flat density pedestal with high separatrix density obtained in the high-power plasma in CFETR would make the operational point close to the ballooning boundary, which is considered to help destabilize ballooning instabilities and facilitate the access to the grassy ELM regime.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Randomized Sketching Algorithms for Low-Memory Dynamic Optimization

This paper develops a novel limited-memory method to solve dynamic optimization problems. The memory requirements for such problems often present a major obstacle, particularly for problems with PDE constraints such as optimal flow control, full waveform inversion, and optical tomography. In these problems, PDE constraints uniquely determine the state of a physical system for a given control; the goal is to find the value of the control that minimizes an objective. While the control is often low dimensional, the state is typically more expensive to store. This paper suggests using randomized matrix approximation to compress the state as it is generated and shows how to use the compressed state to reliably solve the original dynamic optimization problem. Concretely, the compressed state is used to compute approximate gradients and to apply the Hessian to vectors. The approximation error in these quantities is controlled by the target rank of the sketch. This approximate first- and second-order information can readily be used in any optimization algorithm. As an example, we develop a sketched trust-region method that adaptively chooses the target rank using a posteriori error information and provably converges to a stationary point of the original problem. Numerical experiments with the sketched trust-region method show promising performance on challenging problems such as the optimal control of an advection-reaction-diffusion equation and the optimal control of fluid flow past a cylinder.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Semi-Analytic Functions to Calculate the Deposition Coefficients for Ice Crystal Vapor Growth in Bin and Bulk Microphysical Models

Numerical cloud models require estimates of the vapor growth rate for ice crystals. Current bulk and bin microphysical parameterizations generally assume that vapor growth is diffusion limited, though some parameterizations include the influence of surface attachment kinetics through a constant deposition coefficient. A parameterization for variable deposition coefficients is provided herein. The parameterization is an explicit function of the ambient ice supersaturation and temperature, and an implicit function of crystal dimensions and pressure. The parameterization is valid for variable surface types including growth by dislocations and growth by step nucleation. Deposition coefficients are predicted for the two primary growth directions of crystals, allowing for the evolution of the primary habits. Comparisons with benchmark calculations of instantaneous mass growth indicate that the parameterization is accurate to within a relative error of 1%. Parcel model simulations using Lagrangian microphysics as a benchmark indicate that the bulk parameterization captures the evolution of mass mixing ratio and fall speed with typical relative errors of less than 10%, whereas the average axis lengths can have errors of up to 20%. The bin model produces greater accuracy with relative errors often less that 10%. The deposition coefficient parameterization can be used in any bulk and bin scheme, with low error, if an equivalent volume spherical radius is provided.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Improved Prediction of Cold-Air Pools in the Weather Research and Forecasting Model Using a Truly Horizontal Diffusion Scheme for Potential Temperature

The terrain-following vertical coordinate system used by many atmospheric models, including the Weather Research and Forecasting (WRF) Model, is prone to errors in regions of complex terrain. These errors stem, in part, from the calculation of horizontal gradients within the diffusion term of the momentum or scalar evolution equations. In WRF, such gradients can be calculated along coordinate surfaces, or using metric terms that help account for grid skewness. However, neither of these options ensures a truly horizontal gradient calculation, especially if a grid cell is skewed enough that the heights of the neighboring grid points used in the calculation fall outside the vertical range of the cell. In this work, an improved scheme that uses Taylor series approximations to vertically interpolate variables to the level necessary for a truly horizontal gradient calculation is implemented in WRF for the diffusion of potential temperature. The scheme is validated using an atmosphere-at-rest configuration, in which spurious flows develop only as a result of numerical errors and can thus be used as a proxy for model performance. Following validation, the method is applied to the simulation of cold-air pools (CAPs), which occur in regions of complex terrain and are characterized by strong near-surface temperature gradients. Using the truly horizontal scheme, idealized simulations demonstrate reduced numerical mixing in a quiescent CAP, and a realistic case study in the Columbia River basin shows a reduction in positive wind speed bias by up to roughly 20% compared to observations from the Second Wind Forecast Improvement Project.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2016

Large Eddy Simulation of a Supercritical Fuel Jet in Cross Flow using GPU-Acceleration

Fuel is routinely injected into combustion chambers at elevated pressures resulting in formation of supercritical fluid flow. The dispersion of fuel and the combustion processes are significantly different in high pressure conditions as the raditional liquid atomization and evaporation are replaced by diffusion-dominated mixing. Modeling supercritical flow is challenging due to the complex thermodynamics and transport properties of the fluids and in most cases high fidelity numerical simulations are prohibitively expensive. However, numerical investigations must incorporate the flow properties appropriate for the regime for accurate description of the physical processes involved. In this paper, we consider real-fluid properties and simulate the turbulent mixing of fuel jet in cross flow at high ambient pressure. In order to make efficient use of the computer resources and reduce the time to solution, without compromising the resolution requirements, the real-fluid property routines are accelerated via Graphics Processing Unit (GPU) computation. The numerical simulations performed at different resolutions suggest that the high fidelity computations with refined mesh are essential to capture the non-linear dynamics of vortex evolution downstream of the fuel jet and signifies the necessity for an accelerated code. The code is accelerated using the Kokkos C++ library and is demonstrated to be about 2 times faster than the non-accelerated version. Considerable computational cost associated with the thermodynamics routines is reduced in the accelerated version. The results also suggest the resource requirements to compute turbulent closures and the need for acceleration of the routines associated with the sub-grid scale closures.

Gottiparthi, Kalyana C.↗
DOE OSTI2018

Dynamical Analysis of Three Distant Trans-Neptunian Objects with Similar Orbits

Here, this paper reports the discovery and orbital characterization of two extreme trans-Neptunian objects (ETNOs), 2016 QV 89 and 2016 QU 89 , which have orbits that appear similar to that of a previously known object, 2013 UH 15 . All three ETNOs have semimajor axes a ≈ 172 au and eccentricities e ≈ 0.77. The angular elements (i, ω, Ω) vary by 6°, 15°, and 49°, respectively, between the three objects. The two new objects add to the small number of TNOs currently known to have semimajor axes between 150 and 250 au, and they serve as an interesting dynamical laboratory to study the outer realm of our solar system. Using a large ensemble of numerical integrations, we find that the orbits are expected to reside in close proximity in the (a, e) phase plane for roughly 100 Myr before diffusing to more separated values. We find that an explanation for the orbital configuration of the bodies as a collision product is disfavored. We then explore other scenarios that could influence their orbits. With aphelion distances over 300 au, the orbits of these ETNOs extend far beyond the classical Kuiper Belt and an order of magnitude beyond Neptune. As a result, their orbital dynamics can be affected by the proposed new solar system member, referred to as Planet Nine in this work. With perihelion distances of 35–40 au, these orbits are also influenced by resonant interactions with Neptune. Furthermore, a full assessment of any possible new solar system planets must thus take into account this emerging class of TNOs.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2018

Applying Legendre wavelet method with Tikhonov regularization for one-dimensional time-fractional diffusion equations

In this paper, a new method based on two-dimensional Legendre wavelet basis is proposed to solve time-fractional diffusion equations. This technique is used to convert the problem into a system of linear algebraic equations via expanding the required approximation based on the Legendre wavelet basis. The effectiveness of the proposed method is examined by comparing the numerical results with other methods. When the desired system is large, it is ill-conditioned; in this case, Tikhonov regularization method, with discrepancy principle for finding the regularization parameter, is applied to stabilize the solution.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Impact of a Bluff Body on a Pressurized Oxy-fuel Flame

Designing an effective burner is vital for the development of pressurized oxy-fuel combustion technologies. In the present work, turbulent jet diffusion burners are adopted for a pressurized oxy-combustor, with a bluff-body employed to create a recirculation zone, thereby stabilizing the flame in such a combustor. The objective of this numerical study is to perform a systematic analysis of the characteristics of such a pressurized non-premixed flame. Specifically, a 15-bar pressurized oxy-fuel combustor of power 100 kWth is modeled by means of the Ansys FLUENT commercial platform, using the Reynolds-averaged Navier-Stokes (RANS) approach. The present work focuses on identifying the aerothermodynamic features of the pressurized oxy-fuel burner with a disk-shape bluff-body. It is shown that the fuel-to-oxidizer stream momentum ratio has a great impact on the temperature profile of the down-fired, co-axial, pressurized oxy-coal, diffusion flame. A parametric study of the blockage ratio of the burner identifies an optimal range for this pressurized burner.

Li, Lei↗
DOE OSTI2016

Diagnosing Model Errors in Simulation of Solar Radiation on Inclined Surfaces

Transposition models have been widely used in the solar energy industry to simulate solar radiation on inclined PV panels. Following numerous studies comparing the performance of transposition models, this paper aims to understand the quantitative uncertainty in the state-of-the-art transposition models and the sources leading to the uncertainty. Our results show significant differences between two highly used isotropic transposition models with one substantially underestimating the diffuse plane-of-array (POA) irradiances when diffuse radiation is perfectly isotropic. In the empirical transposition models, the selection of empirical coefficients and land surface albedo can both result in uncertainty in the output. This study can be used as a guide for future development of physics-based transposition models.

14 SOLAR ENERGY↗
DOE OSTI2022

Editorial: Particulate Matter Emissions From Conventional and Reformulated Fuel Combustion: Advances in Experiments and Simulations

Particulate matter (PM or soot) emissions generated by combustion of conventional and reformulated fuels adversely impact the environment and human health (Bond et al., 2013; Landrigan et al., 2018; World Health Organization (WHO), 2016), generating public awareness and motivating efforts towards the mitigation of their harmful effects. Soot formation is one of the most complex phenomena in combustion, involving interactions between combustion chemistry, fluid mechanics, mass/heat transport, and particle dynamics, spanning different spatial and temporal scales. A fundamental understanding of soot formation process is thus necessary to achieve a strong reduction of PM emissions and design cleaner and more efficient combustion systems. This has motivated a longstanding and ongoing research activity aimed at improving our understanding of the physical and chemical processes involved in soot formation, well reviewed in these recent works (Wang and Chung, 2019; Michelsen et al., 2020; Martin et al., 2022). Despite the wide interest, the transition from gas-phase molecules to incipient soot particles is still elusive and the successive particle growth and oxidation processes are far from being fully understood, especially in conditions relevant to real-world applications. Recent advances in combustion PM emission diagnostic and computational capabilities helped in improving the predictability of fundamental chemical and aerosol models for practical applications, thus tackling some of the above-mentioned challenges. The aim of this research topic is to display the ongoing research efforts in addressing the existing gaps on particulate formation from various fuel sources and in conditions typical of practical combustion applications (e.g. flames, engines, pool fires), through both experimental and numerical approaches.

42 ENGINEERING↗
DOE OSTI2023

Jacobian-free Newton–Krylov method for the simulation of non-thermal plasma discharges with high-order time integration and physics-based preconditioning

A preconditioning framework for the numerical simulation of non-thermal streamer discharges is developed using the Jacobian-free Newton-Krylov (JFNK) method. A reduced plasma fluid model is considered, consisting of electrons, one positive ion, one negative ion, and the electrostatic potential. Here, the plasma kinetics model includes ionization, electron-ion recombination, electron attachment, electron detachment, and ion-ion recombination. The governing equations are made dimensionless, discretized in space with finite differences, and integrated in time with a fully implicit method based on high-order backward differentiation formulas. The preconditioning framework is based on a linearized form of the governing equations and physics-based operator splitting. The efficiency of the preconditioning strategy is assessed through two test cases: streamer propagation between parallel plates and an axisymmetric pin-to-pin discharge. The fully implicit approach overcomes traditional restrictions in the time step size due to processes such as electron drift, electron diffusion, and dielectric relaxation. Excellent performance is observed through relevant statistics of the JFNK solver, although the number of linear iterations increases for the pin-to-pin discharge when nonlinear numerical boundary conditions are imposed at the electrodes. Performance studies show scalability with O(100-1000) processors for O(10M) unknowns with ample room for optimization.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Performance of high-order Godunov-type methods in simulations of astrophysical low Mach number flows

High-order Godunov methods for gas dynamics have become a standard tool for simulating different classes of astrophysical flows. Their accuracy is mostly determined by the spatial interpolant used to reconstruct the pair of Riemann states at cell interfaces and by the Riemann solver that computes the interface fluxes. In most Godunov-type methods, these two steps can be treated independently, so that many different schemes can in principle be built from the same numerical framework. Because astrophysical simulations often test out the limits of what is feasible with the computational resources available, it is essential to find the scheme that produces the numerical solution with the desired accuracy at the lowest computational cost. However, establishing the best combination of numerical options in a Godunov-type method to be used for simulating a complex hydrodynamic problem is a nontrivial task. In fact, formally more accurate schemes do not always outperform simpler and more diffusive methods, especially if sharp gradients are present in the flow. For this work, we used our fully compressible Seven-League Hydro (SLH) code to test the accuracy of six reconstruction methods and three approximate Riemann solvers on two- and three-dimensional (2D and 3D) problems involving subsonic flows only. We considered Mach numbers in the range from 10 −3 to 10 −1 , which are characteristic of many stellar and geophysical flows. In particular, we considered a well-posed, 2D, Kelvin–Helmholtz instability problem and a 3D turbulent convection zone that excites internal gravity waves in an overlying stable layer. Although the different combinations of numerical methods converge to the same solution with increasing grid resolution for most of the quantities analyzed here, we find that (i) there is a spread of almost four orders of magnitude in computational cost per fixed accuracy between the methods tested in this study, with the most performant method being a combination of a low-dissipation Riemann solver and a sextic reconstruction scheme; (ii) the low-dissipation solver always outperforms conventional Riemann solvers on a fixed grid when the reconstruction scheme is kept the same; (iii) in simulations of turbulent flows, increasing the order of spatial reconstruction reduces the characteristic dissipation length scale achieved on a given grid even if the overall scheme is only second order accurate; (iv) reconstruction methods based on slope-limiting techniques tend to generate artificial, high-frequency acoustic waves during the evolution of the flow; and (v) unlimited reconstruction methods introduce oscillations in the thermal stratification near the convective boundary, where the entropy gradient is steep.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Data-driven learning of nonlocal physics from high-fidelity synthetic data

A key challenge to nonlocal models is the analytical complexity of deriving them from first principles, and frequently their use is justified a posteriori. Here, we extract nonlocal models from data, circumventing these challenges and providing data-driven justification for the resulting model form. Extracting data-driven surrogates is a major challenge for machine learning (ML) approaches, due to nonlinearities and lack of convexity — it is particularly challenging to extract surrogates which are provably well-posed and numerically stable. Our scheme not only yields a convex optimization problem, but also allows extraction of nonlocal models whose kernels may be partially negative while maintaining well-posedness even in small-data regimes. To achieve this, based on established nonlocal theory, we embed in our algorithm sufficient conditions on the non-positive part of the kernel that guarantee well-posedness of the learnt operator. These conditions are imposed as inequality constraints to meet the requisite conditions of the nonlocal theory. We demonstrate this workflow for a range of applications, including reproduction of manufactured nonlocal kernels; numerical homogenization of Darcy flow associated with a heterogeneous periodic microstructure; nonlocal approximation to high-order local transport phenomena; and approximation of globally supported fractional diffusion operators by truncated kernels.

42 ENGINEERING↗
DOE OSTI2023

Laser heating and evaporation of a single droplet

The laser technology is being abundantly studied for controlled energy deposition for a range of applications in aerodynamic flow control, material processing, ignition, and combustion. The absorption of laser radiation by liquid droplets affects further propagation of laser in the atmosphere and causes bleaching of suspended droplets while the ignition and combustion characteristics in combustors are influenced by the evaporation rate of the sprayed fuel. In this work, we present a multi-dimensional mathematical model built on OpenFOAM for laser heating and evaporation of a single droplet in the diffusion dominated regime taking into account absorption of the laser radiation, evaporation process and vapor flow dynamics. The developed solver is validated against available experimental and numerical data for the ethanol and water droplet heating and evaporation. For continuous heating the peak temperature is established by the balance of cooling, evaporation and heating and results in high temperature for larger droplets. It has been shown that for heating by a single laser pulse the maximum temperature of droplets depends only on the peak intensity of the laser radiation. Furthermore, for the peak irradiance close to the transition to the boiling regime, temporal dynamics of the droplet temperature is independent of the droplet size. With proper normalization of time, the dynamics of the droplet shrinkage and cooling is shown to be independent of droplet sizes and peak laser intensities. The influence of cooling and evaporation processes on droplet heating was found to be controlled by the pulse repetition rate for repeated pulse operation.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Journal paper

Laser technology is being widely studied for controlled energy deposition for a range of applications, including flow control, ignition, combustion, and diagnostics. The absorption and scattering of laser radiation by liquid droplets in aerosols affects propagation of the laser beam in the atmosphere, while the ignition and combustion characteristics in combustion chambers are influenced by the evaporation rate of the sprayed fuel. In this work, we present a mathematical model built on OpenFOAM for laser heating and evaporation of a single droplet in the diffusion-dominated regime taking into account absorption of the laser radiation, evaporation process, and vapor flow dynamics. The developed solver is validated against available experimental and numerical data for heating and evaporation of ethanol and water droplets. The two main regimes—continuous and pulsed laser heating—are explored. For continuous laser heating, the peak temperature is higher for larger droplets. For pulsed laser heating, when the peak irradiance is close to transition to the boiling regime, the temporal dynamics of the droplet temperature does not depend on the droplet size. With the empirical normalization of time, the dynamics of the droplet shrinkage and cooling are found to be independent of droplet sizes and peak laser intensities.

42 ENGINEERING↗
DOE OSTI2016

A CAREFULLY CHARACTERIZED AND TRACKED TRANS-NEPTUNIAN SURVEY: THE SIZE DISTRIBUTION OF THE PLUTINOS AND THE NUMBER OF NEPTUNIAN TROJANS

The trans-Neptunian objects (TNOs) preserve evidence of planet building processes in their orbital and size distributions. While all populations show steep size distributions for large objects, a relative deficit of Neptunian trojans and scattering objects with diameters of D < 100 km has been detected. We investigated this deficit with a 32 square degree survey, in which we detected 77 TNOs that are brighter than a limiting r-band magnitude of 24.6. Our plutino sample (18 objects in 3:2 mean-motion resonance with Neptune) shows a deficit of D < 100 km objects, rejecting a single power-law size distribution at >99% confidence. Combining our survey with the Canada–France Ecliptic Plane Survey, we perform a detailed analysis of the allowable parameters for the plutino size distribution, including knees and divots. We surmise the existence of 9000 ± 3000 plutinos with an absolute magnitude of H {sub r} ≤ 8.66 and 37000{sub −10000}{sup +12000} with H {sub r} ≤ 10.0 (95% confidence). Our survey also discovered one temporary Uranian trojan, one temporary Neptunian trojan, and one stable Neptunian trojan, for which we estimate populations of 110{sub −100}{sup +500}, 210{sub −200}{sup +900}, and 150{sub −140}{sup +600} with H {sub r} ≤ 10.0, respectively. All three populations are thus less numerous than the main belt asteroids (592 asteroids with H {sub r} ≤ 10.0). With such population sizes, the temporary Neptunian trojans cannot be previously stable trojans diffusing out of the resonance now; they must be recently captured Centaurs or scattering objects. As the bias against the detection of objects grows with larger semimajor axes, our discovery of three 3:1 resonators and one 4:1 resonator adds to the growing evidence that the high-order resonances are far more populated than is typically predicted.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

A Coarse-Mesh Nonlinear Diffusion Acceleration Scheme with Local Refinement for Neutron Transport Calculations

The coarse-mesh nonlinear diffusion acceleration (CM-NDA) technique, or commonly known as coarse-mesh finite difference (CMFD), is one of the most widely used acceleration methods for numerical transport calculations. Although CM-NDA is very effective to reduce the iteration number of neutron transport sweep, it can sometimes become unstable, in particularly when the coarse mesh size becomes large. Over the last two decades a number of ad hoc techniques have been developed to stabilize the CM-NDA scheme. In this paper, we present a new scheme, LR-NDA, which is based on CM-NDA with local refinement. Within the CM-NDA framework, the LR-NDA scheme incorporates solving an additional local boundary-value problem (BVP) of the neutron flux on each individual coarse mesh cell, yielding a finer flux profile than CMNDA. Our assessments show that this new scheme can significantly improve the effectiveness of CM-NDA, and more importantly it is very stable even for extremely high optical thickness. A great feature of LR-NDA is that it is fully adaptive, which means that it can be easily applied to any local region of the problem domain, and local refinement can be performed using any numerical method (e.g., finite difference, finite element, or spectral element, etc.). (authors)

42 ENGINEERING↗