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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 343 records · Page 19
All sourcesNASA NTRSDOE OSTI
NASA NTRS1995

Grains in ionized nebulae: Spectral line diagnostics

The depletion of condensable elements onto grains in gaseous nebulae can provide evidence that dust is well mixed with the ionized gas. Al and CA are two of the most depleted elements in the general interstellar medium, and it is therefore important to measure their abundances within the ionized region of nebulae. We compute a large grid of photoionization models and identify sets of line ratios which are relatively insensitive to stellar and nebular parameters, and are thus excellent diagnostics for determining relative abundances. Based on the absence of the ((Ca II) lambda lambda 291, 7324 doublet and the detection of Al II) lambda lambda 2660, 2669 in the ultraviolet, we determine the extent of aluminum and calcium depletion onto grains in NGC 7027 and the Orion Nebula. Our results show a approximately 0.3 dex depletion for Al, but a depletion of more than two and a half orders of magnitude for Ca. A similar calculation based on Mg II lambda 2798 yields roughly a 0.8 dex depletion for Mg. This reaffirms the discrepancy between depletion determined from high and low ionization Mg lines. We also find evidence for a 'depletion gradient' in Ca in NGC 7027, since the calcium depletion we infer for the outer, more neutral regions using (Ca II) is somewhat higher than that inferred for the inner high-ionization region, using (Ca v). This gradient can test current models of the survival of grains within hot ionized gas.

Kingdon, J.↗
DOE OSTI2021

Impacts of Varying Concentrations of Cloud Condensation Nuclei on Deep Convective Cloud Updrafts—A Multimodel Assessment

Abstract This study presents results from a model intercomparison project, focusing on the range of responses in deep convective cloud updrafts to varying cloud condensation nuclei (CCN) concentrations among seven state-of-the-art cloud-resolving models. Simulations of scattered convective clouds near Houston, Texas, are conducted, after being initialized with both relatively low and high CCN concentrations. Deep convective updrafts are identified, and trends in the updraft intensity and frequency are assessed. The factors contributing to the vertical velocity tendencies are examined to identify the physical processes associated with the CCN-induced updraft changes. The models show several consistent trends. In general, the changes between the High-CCN and Low-CCN simulations in updraft magnitudes throughout the depth of the troposphere are within 15% for all of the models. All models produce stronger (~+5%–15%) mean updrafts from ~4–7 km above ground level (AGL) in the High-CCN simulations, followed by a waning response up to ~8 km AGL in most of the models. Thermal buoyancy was more sensitive than condensate loading to varying CCN concentrations in most of the models and more impactful in the mean updraft responses. However, there are also differences between the models. The change in the amount of deep convective updrafts varies significantly. Furthermore, approximately half the models demonstrate neutral-to-weaker (~−5% to 0%) updrafts above ~8 km AGL, while the other models show stronger (~+10%) updrafts in the High-CCN simulations. The combination of the CCN-induced impacts on the buoyancy and vertical perturbation pressure gradient terms better explains these middle- and upper-tropospheric updraft trends than the buoyancy terms alone.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS1997

Direct Numerical Simulation of Incompressible Pipe Flow Using a B-Spline Spectral Method

A numerical method based on b-spline polynomials was developed to study incompressible flows in cylindrical geometries. A b-spline method has the advantages of possessing spectral accuracy and the flexibility of standard finite element methods. Using this method it was possible to ensure regularity of the solution near the origin, i.e. smoothness and boundedness. Because b-splines have compact support, it is also possible to remove b-splines near the center to alleviate the constraint placed on the time step by an overly fine grid. Using the natural periodicity in the azimuthal direction and approximating the streamwise direction as periodic, so-called time evolving flow, greatly reduced the cost and complexity of the computations. A direct numerical simulation of pipe flow was carried out using the method described above at a Reynolds number of 5600 based on diameter and bulk velocity. General knowledge of pipe flow and the availability of experimental measurements make pipe flow the ideal test case with which to validate the numerical method. Results indicated that high flatness levels of the radial component of velocity in the near wall region are physical; regions of high radial velocity were detected and appear to be related to high speed streaks in the boundary layer. Budgets of Reynolds stress transport equations showed close similarity with those of channel flow. However contrary to channel flow, the log layer of pipe flow is not homogeneous for the present Reynolds number. A topological method based on a classification of the invariants of the velocity gradient tensor was used. Plotting iso-surfaces of the discriminant of the invariants proved to be a good method for identifying vortical eddies in the flow field.

Loulou, Patrick↗
NASA NTRS1993

Advances in Studies of Electrode Kinetics and Mass Transport in AMTEC Cells (abstract)

Previous work reported from JPL has included characterization of electrode kinetics and alkali atom transport from electrodes including Mo, W, WRh(sub x), WPt(sub x)(Mn), in sodium AMTEC cells and vapor exposure cells, and Mo in potassium vapor exposure cells. These studies were generally performed in cells with small area electrodes (about 1 to 5 cm(sup 2)), and device geometry had little effect on transport. Alkali diffusion coefficients through these electrodes have been characterized, and approximate surface diffusion coefficients derived in cases of activated transport. A basic model of electrode kinetic at the alkali metal vapor/porous metal electrode/alkali beta'-alumina solid electrolyte three phase boundary has been proposed which accounts for electrochemical reaction rates with a collision frequency near the three phase boundary and tunneling from the porous electrode partially covered with adsorbed alkali metal atoms. The small electrode effect in AMTEC cells has been discussed in several papers, but quantitative investigations have described only the overall effect and the important contribution of electrolyte resistance. The quantitative characterization of transport losses in cells with large area electrodes has been limited to simulations of large area electrode effects, or characterization of transport losses from large area electrodes with significant longitudinal temperature gradients. This paper describes new investigations of electrochemical kinetics and transport, particularily with WPt(sub 3.5) electrodes, including the influence of electrode size on the mass transport loss in the AMTEC cell. These electrodes possess excellent sodium transport properties making verification of device limitations on transport much more readily attained.

electrode kinetics alkali atom transport transport↗
DOE OSTI2021

A machine learning approach for efficient multi-dimensional integration

Many physics problems involve integration in multi-dimensional space whose analytic solution is not available. The integrals can be evaluated using numerical integration methods, but it requires a large computational cost in some cases, so an efficient algorithm plays an important role in solving the physics problems. We propose a novel numerical multi-dimensional integration algorithm using machine learning (ML). After training a ML regression model to mimic a target integrand, the regression model is used to evaluate an approximation of the integral. Then, the difference between the approximation and the true answer is calculated to correct the bias in the approximation of the integral induced by ML prediction errors. Because of the bias correction, the final estimate of the integral is unbiased and has a statistically correct error estimation. Three ML models of multi-layer perceptron, gradient boosting decision tree, and Gaussian process regression algorithms are investigated. The performance of the proposed algorithm is demonstrated on six different families of integrands that typically appear in physics problems at various dimensions and integrand difficulties. The results show that, for the same total number of integrand evaluations, the new algorithm provides integral estimates with more than an order of magnitude smaller uncertainties than those of the VEGAS algorithm in most of the test cases.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1993

Advances in Studies of Electrode Kinetics and Mass Transport in AMTEC Cells

Previous work reported from JPL has included characterization of electrode kinetics and alkali atom transport from electrodes including Mo, W, WRh x (Mn), in sodium AMTEC cells and vapor exposure cells; and Mo in potassium vapor exposure cells. These studies were generally performed in cells with small area electrodes (about 1 to 5 cm 2 ), and device geometry had little effect on transport. Alkali metal diffusion coefficients through these electrodes have been characterized, and approximate surface diffusion coefficients were derived in cases of activated transport. A basic model of electrode kinetics and transport at the alkali metal vapor/pourous metal electrode/alkali beta"-alumina solid electrolyte (BASE) three phase boundary has been proposed which accounts for electrochemical reaction rates with a collision frequency near the three phase boundary and tunneling from the porous electrode partially covered with adsorbed alkali metal atoms. The small electrode effect in AMTEC cells has been discussed in several papers, but quantitative investigations have described only the overall effect and the important contribution of electrolyte resistance. The quantitative characterization of transport losses in cells with large area electrodes has been limited to simulations of large area electrode effects, or characterization of transport losses from large area electrodes with significant longitudinal temperature gradients. This paper describes new investigations of electrochemical kinetics and transport, with four 14.4 cm 2 WPt 3.5 electrodes, including the influence of electrode size on the mass transport loss in the AMTEC cell. These electrodes exhibit very slow sintering, as well as excellent sodium transport properties, making them attractive candidates for AMTEC power conversion use. However, the facile sodium transport in WPt 3.5 electrodes makes characterization of the transport process difficult.

electrode↗
NASA NTRS1994

Large-scale characteristics of interstellar dust from COBE DIRBE observations

Observations from the COBE Diffuse Infrared Background Experiment of the 140 and 240 micrometer emissions from the Galatic plane region (absolute value of b less than 10 deg) are combined with radio surveys that trace the molecular (H2), neutral atomic (H I), and extended low-density (n(sub e) approximately 10 to 100/cm(exp 3)) ionized (H II) gas phases of the interstellar medium to derive physical conditions such as the dust temperature, dust-to-gas mass ratio, and far-infrared emissivity (1) averaged over these gas phases along each line of sight and (2) within each of these three gas phases. This analysis shows large-scale longitudinal and latitudinal gradients in the dust temperature and a decrease in dust temperature with increasing Galactocentric distance. The derived dust temperatures are significantly different from those derived in similar analyses using the Infrared Astronomical Satellite (IRAS) 60 and 100 micrometer data, suggesting that small (5 A approximately less than radius approximately less than 200 A) transiently heated dust particles contribute significantly o the Galactic 60 micrometer emission. It is found that 60% to 75% of the far-infrared luminosity arises from cold (approximately 17 to 22 K) dust associated with diffuse H I clouds, 15% to 30% from cold (approximately 19 K) dust associated with molecular gas, and less than 10% from warm (approximately 29 K) dust in extended low-density H II regions, consistent with the results of the IRAS analyses of the Galactic 60 and 100 micrometer emission. Within 2 deg of longitude of the Galactic center, the derived gas-to-dust mass ratio along the line of sight, G(sub d), reverses its general trend of decreasing G(sub d) toward the inner Galaxy and increases by a factor of approximately 2 to 3 toward the Galactic center. One possible explanation for this result is that the ratio of H2 column density to (12)CO intensity is lower in the Galactic center region than in the Galactic disk.

Sodroski, T. J.↗
DOE OSTI2022

Global stochastic optimization of stellarator coil configurations

In the construction of a stellarator, the manufacturing and assembling of the coil system is a dominant cost. These coils need to satisfy strict engineering tolerances, and if those are not met the project could be cancelled as in the case of the National Compact Stellarator Experiment (NCSX) project. Therefore, our goal is to find coil configurations that increase construction tolerances without compromising the performance of the magnetic field. In this paper, we develop a gradient-based stochastic optimization model which seeks robust stellarator coil configurations in high dimensions. In particular, we design a two-step method: first, we perform an approximate global search by a sample efficient trust-region Bayesian optimization; second, we refine the minima found in step one with a stochastic local optimizer. To this end, we introduce two stochastic local optimizers: BFGS applied to the sample average approximation; and Adam, equipped with a control variate for variance reduction. Numerical simulations performed on a W7-X-like coil configuration demonstrate that our global optimization approach finds a variety of promising local solutions at less than 0.1% of the cost of previous work, which considered solely local stochastic optimization.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS2013

RF Reference Switch for Spaceflight Radiometer Calibration

The goal of this technology is to provide improved calibration and measurement sensitivity to the Soil Moisture Active Passive Mission (SMAP) radiometer. While RF switches have been used in the past to calibrate microwave radiometers, the switch used on SMAP employs several techniques uniquely tailored to the instrument requirements and passive remote-sensing in general to improve radiometer performance. Measurement error and sensitivity are improved by employing techniques to reduce thermal gradients within the device, reduce insertion loss during antenna observations, increase insertion loss temporal stability, and increase rejection of radar and RFI (radio-frequency interference) signals during calibration. The two legs of the single-pole double-throw reference switch employ three PIN diodes per leg in a parallel-shunt configuration to minimize insertion loss and increase stability while exceeding rejection requirements at 1,413 MHz. The high-speed packaged diodes are selected to minimize junction capacitance and resistance while ensuring the parallel devices have very similar I-V curves. Switch rejection is improved by adding high-impedance quarter-wave tapers before and after the diodes, along with replacing the ground via of one diode per leg with an open circuit stub. Errors due to thermal gradients in the switch are reduced by embedding the 50-ohm reference load within the switch, along with using a 0.25-in. (approximately equal to 0.6-cm) aluminum prebacked substrate. Previous spaceflight microwave radiometers did not embed the reference load and thermocouple directly within the calibration switch. In doing so, the SMAP switch reduces error caused by thermal gradients between the load and switch. Thermal issues are further reduced by moving the custom, highspeed regulated driver circuit to a physically separate PWB (printed wiring board). Regarding RF performance, previous spaceflight reference switches have not employed high-impedance tapers to improve rejection. The use of open-circuit stubs instead of a via to provide an improved RF short is unique to this design. The stubs are easily tunable to provide high rejection at specific frequencies while maintaining very low insertion loss in-band.

Knuble, Joseph↗
DOE OSTI2021

Coupled physics simulation of fracture in nuclear fuel pellets induced by resistive heating

While it is well known that the UO 2 fuel used in light-water reactors cracks early in its life in the reactor, it is very difficult to collect in-reactor data regarding fuel cracking initiation and propagation to validate fracture models in fuel performance codes. Most fracture data comes from the post-irradiation examination of fuel that has been subjected to long and complex power histories. Replicating the thermal gradients experienced in this fuel to study crack initiation and propagation in a laboratory environment is challenging. This is primarily because the fuel is heated volumetrically by fission, which is difficult to replicate. One way to approximate this volumetric heating out of the reactor is to use electrical resistance (or Joule heating). An electrical conductivity model has been developed and coupled with the existing thermomechanical modeling capability in the BISON nuclear fuel performance code. This will permit simulation of experiments that use resistive heating for the purpose of validating fracture models in BISON. The modeling approach developed here is applied to simulate both historical and current resistive heating experiments on ceramic nuclear fuel.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2024

Optimization using pathwise algorithmic derivatives of electromagnetic shower simulations

Among the well-known methods to approximate derivatives of expectancies computed by Monte-Carlo simulations, averages of pathwise derivatives are often the easiest one to apply. Computing them via algorithmic differentiation typically does not require major manual analysis and rewriting of the code, even for very complex programs like simulations of particle-detector interactions in high-energy physics. However, the pathwise derivative estimator can be biased if there are discontinuities in the program, which may diminish its value for applications. This work integrates algorithmic differentiation into the electromagnetic shower simulation code HepEmShow based on G4HepEm, allowing us to study how well pathwise derivatives approximate derivatives of energy depositions in a sampling calorimeter with respect to parameters of the beam and geometry. We found that when multiple scattering is disabled in the simulation, means of pathwise derivatives converge quickly to their expected values, and these are close to the actual derivatives of the energy deposition. Additionally, we demonstrate the applicability of this novel gradient estimator for stochastic gradient-based optimization in a model example.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS2015

Solar Signals in CMIP-5 Simulations: The Stratospheric Pathway

The 11 year solar-cycle component of climate variability is assessed in historical simulations of models taken from the Coupled Model Intercomparison Project, phase 5 (CMIP-5). Multiple linear regression is applied to estimate the zonal temperature, wind and annular mode responses to a typical solar cycle, with a focus on both the stratosphere and the stratospheric influence on the surface over the period approximately 1850-2005. The analysis is performed on all CMIP-5 models but focuses on the 13 CMIP-5 models that resolve the stratosphere (high-top models) and compares the simulated solar cycle signature with reanalysis data. The 11 year solar cycle component of climate variability is found to be weaker in terms of magnitude and latitudinal gradient around the stratopause in the models than in the reanalysis. The peak in temperature in the lower equatorial stratosphere (approximately 70 hPa) reported in some studies is found in the models to depend on the length of the analysis period, with the last 30 years yielding the strongest response. A modification of the Polar Jet Oscillation (PJO) in response to the 11 year solar cycle is not robust across all models, but is more apparent in models with high spectral resolution in the short-wave region. The PJO evolution is slower in these models, leading to a stronger response during February, whereas observations indicate it to be weaker. In early winter, the magnitude of the modeled response is more consistent with observations when only data from 1979-2005 are considered. The observed North Pacific high-pressure surface response during the solar maximum is only simulated in some models, for which there are no distinguishing model characteristics. The lagged North Atlantic surface response is reproduced in both high- and low-top models, but is more prevalent in the former. In both cases, the magnitude of the response is generally lower than in observations.

stratosphere↗
DOE OSTI2020

Accurate prediction of core-level spectra of radicals at density functional theory cost via square gradient minimization and recoupling of mixed configurations

State-specific orbital optimized approaches are more accurate at predicting core-level spectra than traditional linear-response protocols, but their utility had been restricted due to the risk of "variational collapse" down to the ground state. We employ the recently developed square gradient minimization algorithm to reliably avoid variational collapse and study the effectiveness of orbital optimized density functional theory (DFT) at predicting second period element 1s core-level spectra of open-shell systems. Several density functionals (including SCAN, B3LYP, and ωB97X-D3) are found to predict excitation energies from the core to singly occupied levels with high accuracy (≤0.3 eV RMS error) against available experimental data. Higher excited states are, however, more challenging by virtue of being intrinsically multiconfigurational. We thus present a configuration interaction inspired route to self-consistently recouple single determinant mixed configurations obtained from DFT, in order to obtain approximate doublet states. This recoupling scheme is used to predict the C K-edge spectra of the allyl radical, the O K-edge spectra of CO + , and the N K-edge of NO 2 with high accuracy relative to experiment, indicating substantial promise in using this approach for the computation of core-level spectra for doublet species [vs more traditional time dependent DFT, equation of motion coupled cluster singles and doubles (EOM-CCSD), or using unrecoupled mixed configurations]. Finally, we also present general guidelines for computing core-excited states from orbital optimized DFT.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1943

Heat Transfer Through Turbulent Friction Layers

The "general Prandtl number" Pr(exp 1) - A(sub q)/A Pr, aside from the Reynolds number determines the ratio of turbulent to molecular heat transfer, and the temperature distribution in turbulent friction layers. A(sub q) = exchange coefficient for heat; A = exchange coefficient for momentum transfer. A formula is derived from the equation defining the general Prandtl number which describes the temperature as a function of the velocity. For fully developed thermal boundary layers all questions relating to heat transfer to and from incompressible fluids can be treated in a simple manner if the ratio of the turbulent shear stress to the total stress T(sub t)/T in the layers near the wall is known, and if the A(sub q)/A can be regarded as independent of the distance from the wall. The velocity distribution across a flat smooth channel and deep into the laminar sublayer was measured for isothermal flow to establish the shear stress ratio T(sub t)/T and to extend the universal wall friction law. The values of T(sub t)/T which resulted from these measurements can be approximately represented by a linear function of the velocity in the laminar-turbulent transition zone. The effect of the temperature relationship of the material values on the flow near the wall is briefly analyzed. It was found that the velocity at the laminar boundary (in contrast to the thickness of the laminar layer) is approximately independent of the temperature distribution. The temperature gradient at the wall and the distribution of temperature and heat flow in the turbulent friction layers were calculated on the basis of the data under two equations. The derived formulas and the figures reveal the effects of the Prandtl number, the Reynolds number, the exchange quantities and the temperature relationship of the material values.

Reichardt, H.↗
NASA NTRS1993

Energy transfer and constrained simulations in isotropic turbulence

The defining characteristic of turbulent flows is their ability to dissipate energy, even in the limit of zero viscosity. The Euler equations, if constrained in such a way that the velocity derivatives remain bounded, conserve energy. But when they arise as the limit of the Navier-Stokes (NS) equations, when the Reynolds number goes to infinity, there is persuasive empirical evidence that the gradients become singular as just the right function of Re for the dissipation to remain non-zero and to approach a well defined limit. It is generally believed that this limiting value of the dissipation is a property of the Euler equations themselves, independent of the particular dissipative mechanism involved, and that it can be normalized with the large scale properties of the turbulent flow (e.g. the kinetic energy per unit volume u'(exp 2)/2, and the integral scale L) without reference to the Reynolds number or to other dissipative quantities. This is usually taken to imply that the low wave number end of the energy spectrum, far from the dissipative range, is also independent of the particular mechanism chosen to dispose of the energy transfer. In the following sections, we present some numerical experiments on the effect of substituting different dissipation models into the truncated Euler equations. We will see that the effect is mainly felt in the 'near dissipation' range of the energy spectrum, but that this range can be quite wide in some cases, contaminating a substantial range of wave numbers. In the process, we will develop a 'practical' approximation to the subgrid energy transfer in isotropic turbulence, and we will gain insight into the structure of the nonlinear interactions among turbulent scales of comparable size, and into the nature of energy backscatter. Some considerations on future research directions are offered at the end.

Jimenez, Javier↗
DOE OSTI2020

Persistent compositions of non-stoichiometric compounds with low bulk diffusivity: A theory and application to Nb3Sn superconductors

Non-stoichiometric compounds may develop a composition gradient when they are formed by reactive diffusional processes. This paper reports an interesting phenomenon that in compounds with low bulk diffusivities, which rely mainly on grain boundary diffusion for their growth, the final bulk compositions may be far from equilibrium, with a very low bulk diffusivity leading to fixed (persistent) compositions – one such example is Nb 3 Sn, a superconductor. We investigated the microchemistry at the reactive interface using atom probe tomography to clarify the diffusion reaction mechanism for this low-bulk-diffusivity case and thus propose a theory for what determines the compound composition, using Nb 3 Sn as an example for concreteness. Using certain approximations, we derive an explicit analytical equation that illustrates what factors determine its composition profile. We compare our model with the known facts of Nb 3 Sn and see good agreement. In particular, this model predicts that internal oxidation may lead to higher Sn contents than conventional, non-oxidized Nb 3 Sn. Our measurements show that this is indeed true, and that the internally-oxidized Nb 3 Sn also has higher upper critical fields, achieving up to 28.2 T at 4.2 K. We discuss the general applicability of this model to non-stoichiometric compounds with low bulk diffusivity, and propose it as a tool to help in the design and processing of such materials for compositional control.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Nonlinear sparse Bayesian learning for physics-based models

This paper addresses the issue of overfitting while calibrating unknown parameters of over-parameterized physics-based models with noisy and incomplete observations. Here, a semi-analytical Bayesian framework of nonlinear sparse Bayesian learning (NSBL) is proposed to identify sparsity among model parameters during Bayesian inversion. NSBL offers significant advantages over machine learning algorithm of sparse Bayesian learning (SBL) for physics-based models, such as 1) the likelihood function or the posterior parameter distribution is not required to be Gaussian, and 2) prior parameter knowledge is incorporated into sparse learning (i.e. not all parameters are treated as questionable). NSBL employs the concept of automatic relevance determination (ARD) to facilitate sparsity among questionable parameters through parameterized prior distributions. The analytical tractability of NSBL is enabled by employing Gaussian ARD priors and by building a Gaussian mixture-model approximation of the posterior parameter distribution that excludes the contribution of ARD priors. Subsequently, type-II maximum likelihood is executed using Newton's method whereby the evidence and its gradient and Hessian information are computed in a semi-analytical fashion. We show numerically and analytically that SBL is a special case of NSBL for linear regression models. Subsequently, a linear regression example involving multimodality in both parameter posterior pdf and model evidence is considered to demonstrate the performance of NSBL in cases where SBL is inapplicable. Next, NSBL is applied to identify sparsity among the damping coefficients of a mass-spring-damper model of a shear building frame. These numerical studies demonstrate the robustness and efficiency of NSBL in alleviating overfitting during Bayesian inversion of nonlinear physics-based models.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS2004

Relaxation and Preconditioning for High Order Discontinuous Galerkin Methods with Applications to Aeroacoustics and High Speed Flows

This project is about the investigation of the development of the discontinuous Galerkin finite element methods, for general geometry and triangulations, for solving convection dominated problems, with applications to aeroacoustics. Other related issues in high order WENO finite difference and finite volume methods have also been investigated. methods are two classes of high order, high resolution methods suitable for convection dominated simulations with possible discontinuous or sharp gradient solutions. In [18], we first review these two classes of methods, pointing out their similarities and differences in algorithm formulation, theoretical properties, implementation issues, applicability, and relative advantages. We then present some quantitative comparisons of the third order finite volume WENO methods and discontinuous Galerkin methods for a series of test problems to assess their relative merits in accuracy and CPU timing. In [3], we review the development of the Runge-Kutta discontinuous Galerkin (RKDG) methods for non-linear convection-dominated problems. These robust and accurate methods have made their way into the main stream of computational fluid dynamics and are quickly finding use in a wide variety of applications. They combine a special class of Runge-Kutta time discretizations, that allows the method to be non-linearly stable regardless of its accuracy, with a finite element space discretization by discontinuous approximations, that incorporates the ideas of numerical fluxes and slope limiters coined during the remarkable development of the high-resolution finite difference and finite volume schemes. The resulting RKDG methods are stable, high-order accurate, and highly parallelizable schemes that can easily handle complicated geometries and boundary conditions. We review the theoretical and algorithmic aspects of these methods and show several applications including nonlinear conservation laws, the compressible and incompressible Navier-Stokes equations, and Hamilton-Jacobi-like equations.

Shu, Chi-Wang↗