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NASA NTRS1995

Evaluation of numerical schemes for the analysis of sound generation by blade-gust interaction

In this investigation three different numerical algorithms have been utilized to compute the flow about a flat plate in the presence of a transverse gust described by a sinusoidal disturbance. The three schemes include the MacCormack explicit finite difference scheme which is second order accurate in both time and space, the Gottlieb and Turkel modification of MacCormack's scheme which is fourth order accurate in space and second order accurate in time, (referred to as the 2-4 scheme), and a two step scheme developed by Bayliss et al. which has second order temporal accuracy and sixth order spatial accuracy (a 2-6 scheme). The flow field results are obtained with these schemes by using the same code with the only difference being the implementation of the respective solution algorithms. The problem is set up so that the sinusoidal disturbance is imposed at the surface of the flat plate as a surface boundary condition. Thus the problem is treated as scattering problem. The computed results include the time average of the acoustic pressure squared along grid lines five points away from the boundaries; distribution throughout the computational domain is monitored at various times. The numerical results are compared with an exact solution obtained by Atassi, Dusey, and Davis.

Scott, J. N.↗

NASA NTRS1995

Digital modulation schemes for high speed transmission through low bandwidth lowpass analog links

Existing NTSC (National Television System Committee) standard will be phased out and replaced with HDTV (High Definition Television) standard within the next 10 years. Accordingly, the existing video network system operated by NASA will become obsolete and requires either replacement or modification to accommodate digital transmission. Network replacement is extremely expensive, hence, several digital modulation schemes are investigated in this report to accomplish digital transmission over existing analog links saving NASA from the cost of network replacement. There are two competing transmission systems available for HDTV transmission over limited bandwidth channels. The cost and performance of the two competing schemes are remarkably similar. However, the input data rate in such a case is limited to 40 Mbit/s. Transmission of higher data rates is possible using simple signal processing techniques. On the other hand, a third transmission system, multilevel pulse amplitude modulation (M-PAM) is proposed. M-PAM is the first stage of the well known M-VSB. This M-PAM scheme is much simpler and uses the channel more efficiently. The three schemes are compared and preliminary conclusions were made. Despite of several similarities, each modulation scheme has it unique merits. To determine the suitability of each scheme, more investigations and laboratory tests for all schemes are needed.

Andrawis, Alfred S.↗

NASA NTRS1986

An Implicit, Conservative, Zonal-Boundary Scheme for Euler Equation Calculations

A "zonal," or "patched-grid," approach is one in which the flow region of interest is divided into subregions which are then discretized independently, using existing grid generators. The equations of motion are integrated in each subregion in conjunction with zonal-boundary schemes which allow proper information transfer across interfaces that separate subregions. The zonal approach greatly simplifies the treatment of complex geometries and also the addition of grid points to selected regions of the flow. In this study a conservative, zonal-boundary condition that could be used with explicit schemes has been extended so that it can be used with existing second-order accurate implicit integration schemes such as the Beam-Warming and Osher schemes. In the test case considered, the implicit schemes increased the rate of convergence considerably (by a factor of about 30 over that of the explicit scheme). Results demonstrating the time-accuracy of the zonal scheme and the feasibility of performing calculations on zones that move relative to each other are also presented.

Rai, Man Mohan↗

NASA NTRS2002

High-Order Central WENO Schemes for Multi-Dimensional Hamilton-Jacobi Equations

We present new third- and fifth-order Godunov-type central schemes for approximating solutions of the Hamilton-Jacobi (HJ) equation in an arbitrary number of space dimensions. These are the first central schemes for approximating solutions of the HJ equations with an order of accuracy that is greater than two. In two space dimensions we present two versions for the third-order scheme: one scheme that is based on a genuinely two-dimensional Central WENO reconstruction, and another scheme that is based on a simpler dimension-by-dimension reconstruction. The simpler dimension-by-dimension variant is then extended to a multi-dimensional fifth-order scheme. Our numerical examples in one, two and three space dimensions verify the expected order of accuracy of the schemes.

Bryson, Steve↗

NASA NTRS1997

Numerical Schemes for the Hamilton-Jacobi and Level Set Equations on Triangulated Domains

Borrowing from techniques developed for conservation law equations, numerical schemes which discretize the Hamilton-Jacobi (H-J), level set, and Eikonal equations on triangulated domains are presented. The first scheme is a provably monotone discretization for certain forms of the H-J equations. Unfortunately, the basic scheme lacks proper Lipschitz continuity of the numerical Hamiltonian. By employing a virtual edge flipping technique, Lipschitz continuity of the numerical flux is restored on acute triangulations. Next, schemes are introduced and developed based on the weaker concept of positive coefficient approximations for homogeneous Hamiltonians. These schemes possess a discrete maximum principle on arbitrary triangulations and naturally exhibit proper Lipschitz continuity of the numerical Hamiltonian. Finally, a class of Petrov-Galerkin approximations are considered. These schemes are stabilized via a least-squares bilinear form. The Petrov-Galerkin schemes do not possess a discrete maximum principle but generalize to high order accuracy.

Barth, Timothy J.↗

NASA NTRS2006

A Scheme for finding the Front Boundary of an Interplanetary Magnetic Cloud

We developed a scheme for finding the front boundary of an interplanetary magnetic cloud (MC) based on criteria that depend on the possible existence of any one or all of six specific solar wind features. The features that the program looks for, within +/- 2 hours of a preliminarily determined time for the front boundary, estimated either by visual inspection or by an automatic MC identification scheme, are: (1) a sufficiently large directional discontinuity in the interplanetary magnetic field (IMF), (2) existence of a magnetic hole, (3) a significant proton plasma beta drop, (4) a significant proton temperature drop, (5) a marked increase in the IMF's intensity, and (6) a significant decrease in a normalized root-mean-square deviation (RMS)of the magnetic field - where the scheme was tested using 5, 10, 15, and 20 minute averages of the relevant physical quantities, in order to find the optimum average (and RMS) to use. Other criteria, besides these six, were examined and dismissed as not reliable, e.g., plasma speed. The scheme was developed specifically for aiding in forecasting the strength and timing of a geomagnetic storm due to the passage of an interplanetary MC in real-time, but can be used in post ground-data collection for imposition of consistency in choosing a MC's front boundary. The scheme has been extensively tested, first using 80 bona fide MCs over about 9 years of WIND data, and also for 121 MC-like structures as defined by a program that automatically identifies such structures over the same period. Optimum limits for various parameters in the scheme were found by statistical studies of the WIND MCs. The resulting limits can be user-adjusted for other data sets, if desired. Final testing of the 80 MCs showed that for 50 percent of the events the boundary estimates occurred within +/-10 minutes of visually determined times, 80 percent occurred within +/-30 minutes, and 91 percent occur within +/-60 minutes, and three or more individual boundary tests were passed for 88 percent of the total MCs. The scheme and its testing will be described.

Lepping, Ronald P.↗

NASA NTRS2008

The a(3) Scheme--A Fourth-Order Space-Time Flux-Conserving and Neutrally Stable CESE Solver

The CESE development is driven by a belief that a solver should (i) enforce conservation laws in both space and time, and (ii) be built from a non-dissipative (i.e., neutrally stable) core scheme so that the numerical dissipation can be controlled effectively. To initiate a systematic CESE development of high order schemes, in this paper we provide a thorough discussion on the structure, consistency, stability, phase error, and accuracy of a new 4th-order space-time flux-conserving and neutrally stable CESE solver of an 1D scalar advection equation. The space-time stencil of this two-level explicit scheme is formed by one point at the upper time level and three points at the lower time level. Because it is associated with three independent mesh variables (the numerical analogues of the dependent variable and its 1st-order and 2ndorder spatial derivatives, respectively) and three equations per mesh point, the new scheme is referred to as the a(3) scheme. Through the von Neumann analysis, it is shown that the a(3) scheme is stable if and only if the Courant number is less than 0.5. Moreover, it is established numerically that the a(3) scheme is 4th-order accurate.

Chang, Sin-Chung↗

NASA NTRS2008

High-Order Energy Stable WENO Schemes

A new third-order Energy Stable Weighted Essentially NonOscillatory (ESWENO) finite difference scheme for scalar and vector linear hyperbolic equations with piecewise continuous initial conditions is developed. The new scheme is proven to be stable in the energy norm for both continuous and discontinuous solutions. In contrast to the existing high-resolution shock-capturing schemes, no assumption that the reconstruction should be total variation bounded (TVB) is explicitly required to prove stability of the new scheme. A rigorous truncation error analysis is presented showing that the accuracy of the 3rd-order ESWENO scheme is drastically improved if the tuning parameters of the weight functions satisfy certain criteria. Numerical results show that the new ESWENO scheme is stable and significantly outperforms the conventional third-order WENO finite difference scheme of Jiang and Shu in terms of accuracy, while providing essentially nonoscillatory solutions near strong discontinuities.

Yamaleev, Nail K.↗

NASA NTRS2009

Towards an "All Speed" Unstructured Upwind Scheme

In the authors previous studies [1], a time-accurate, upwind finite volume method (ETAU scheme) for computing compressible flows on unstructured grids was proposed. The scheme is second order accurate in space and time and yields high resolution in the presence of discontinuities. The scheme features a multidimensional limiter and multidimensional numerical dissipation. These help to stabilize the numerical process and to overcome the annoying pathological behaviors of upwind schemes. In the present paper, it will be further shown that such multidimensional treatments also lead to a nearly all-speed or Mach number insensitive upwind scheme. For flows at very high Mach number, e.g., 10, local numerical instabilities or the pathological behaviors are suppressed, while for flows at very low Mach number, e.g., 0.02, computation can be directly carried out without invoking preconditioning. For flows in different Mach number regimes, i.e., low, medium, and high Mach numbers, one only needs to adjust one or two parameters in the scheme. Several examples with low and high Mach numbers are demonstrated in this paper. Thus, the ETAU scheme is applicable to a broad spectrum of flow regimes ranging from high supersonic to low subsonic, appropriate for both CFD (computational fluid dynamics) and CAA (computational aeroacoustics).

Loh, Ching Y.↗

NASA NTRS2009

Re-evaluation of an Optimized Second Order Backward Difference (BDF2OPT) Scheme for Unsteady Flow Applications

Recent experience in the application of an optimized, second-order, backward-difference (BDF2OPT) temporal scheme is reported. The primary focus of the work is on obtaining accurate solutions of the unsteady Reynolds-averaged Navier-Stokes equations over long periods of time for aerodynamic problems of interest. The baseline flow solver under consideration uses a particular BDF2OPT temporal scheme with a dual-time-stepping algorithm for advancing the flow solutions in time. Numerical difficulties are encountered with this scheme when the flow code is run for a large number of time steps, a behavior not seen with the standard second-order, backward-difference, temporal scheme. Based on a stability analysis, slight modifications to the BDF2OPT scheme are suggested. The performance and accuracy of this modified scheme is assessed by comparing the computational results with other numerical schemes and experimental data.

Vatsa, Veer N.↗

NASA NTRS2015

High-Resolution NU-WRF Simulations of a Deep Convective-Precipitation System During MC3E: Comparisons Between Goddard Microphysics Schemes and Observations - Part 1

The Goddard microphysics scheme was recently improved by adding a 4th ice class (frozen dropshail). This new 4ICE scheme was implemented and tested in the Goddard Cumulus Ensemble model (GCE) for an intense continental squall line and a moderate,less-organized continental case. Simulated peak radar reflectivity profiles were improved both in intensity and shape for both cases as were the overall reflectivity probability distributions versus observations. In this study, the new Goddard 4ICE scheme is implemented into the regional-scale NASA Unified - Weather Research and Forecasting model (NU-WRF) and tested on an intense mesoscale convective system that occurred during the Midlatitude Continental Convective Clouds Experiment (MC3E). The NU42WRF simulated radar reflectivities, rainfall intensities, and vertical and horizontal structure using the new 4ICE scheme agree as well as or significantly better with observations than when using previous versions of the Goddard 3ICE (graupel or hail) schemes. In the 4ICE scheme, the bin microphysics-based rain evaporation correction produces more erect convective cores, while modification of the unrealistic collection of ice by dry hail produces narrow and intense cores, allowing more slow-falling snow to be transported rearward. Together with a revised snow size mapping, the 4ICE scheme produces a more horizontally stratified trailing stratiform region with a broad, more coherent light rain area. In addition, the NU-WRF 4ICE simulated radar reflectivity distributions are consistent with and generally superior to those using the GCE due to the less restrictive open lateral boundaries

Regional Scale Model↗

NASA NTRS2015

Intercomparison of Martian Lower Atmosphere Simulated Using Different Planetary Boundary Layer Parameterization Schemes

We use the mesoscale modeling capability of Mars Weather Research and Forecasting (MarsWRF) model to study the sensitivity of the simulated Martian lower atmosphere to differences in the parameterization of the planetary boundary layer (PBL). Characterization of the Martian atmosphere and realistic representation of processes such as mixing of tracers like dust depend on how well the model reproduces the evolution of the PBL structure. MarsWRF is based on the NCAR WRF model and it retains some of the PBL schemes available in the earth version. Published studies have examined the performance of different PBL schemes in NCAR WRF with the help of observations. Currently such assessments are not feasible for Martian atmospheric models due to lack of observations. It is of interest though to study the sensitivity of the model to PBL parameterization. Typically, for standard Martian atmospheric simulations, we have used the Medium Range Forecast (MRF) PBL scheme, which considers a correction term to the vertical gradients to incorporate nonlocal effects. For this study, we have also used two other parameterizations, a non-local closure scheme called Yonsei University (YSU) PBL scheme and a turbulent kinetic energy closure scheme called Mellor- Yamada-Janjic (MYJ) PBL scheme. We will present intercomparisons of the near surface temperature profiles, boundary layer heights, and wind obtained from the different simulations. We plan to use available temperature observations from Mini TES instrument onboard the rovers Spirit and Opportunity in evaluating the model results.

Natarajan, Murali↗

NASA NTRS2017

Sensitivity of CONUS Summer Rainfall to the Selection of Cumulus Parameterization Schemes in NU-WRF Seasonal Simulations

This study investigates the sensitivity of daily rainfall rates in regional seasonal simulations over the contiguous United States (CONUS) to different cumulus parameterization schemes. Daily rainfall fields were simulated at 24-km resolution using the NASA-Unified Weather Research and Forecasting (NU-WRF) Model for June-August 2000. Four cumulus parameterization schemes and two options for shallow cumulus components in a specific scheme were tested. The spread in the domain-mean rainfall rates across the parameterization schemes was generally consistent between the entire CONUS and most subregions. The selection of the shallow cumulus component in a specific scheme had more impact than that of the four cumulus parameterization schemes. Regional variability in the performance of each scheme was assessed by calculating optimally weighted ensembles that minimize full root-mean-square errors against reference datasets. The spatial pattern of the seasonally averaged rainfall was insensitive to the selection of cumulus parameterization over mountainous regions because of the topographical pattern constraint, so that the simulation errors were mostly attributed to the overall bias there. In contrast, the spatial patterns over the Great Plains regions as well as the temporal variation over most parts of the CONUS were relatively sensitive to cumulus parameterization selection. Overall, adopting a single simulation result was preferable to generating a better ensemble for the seasonally averaged daily rainfall simulation, as long as their overall biases had the same positive or negative sign. However, an ensemble of multiple simulation results was more effective in reducing errors in the case of also considering temporal variation.

Iguchi, Takamichi↗

NASA NTRS2018

Comparisons of Bin and Bulk Microphysics Schemes in Simulations of Topographic Winter Precipitation with Radar and Radiometer Measurements

The Hebrew University Cloud Model (HUCM) bin scheme and the Thompson bulk scheme in the Weather Research and Forecasting (WRF) model are compared to assess biases often found in simulated brightness temperature and radar reflectivity. Compared to our preceding study that evaluated several bulk schemes in the WRF model, the current study obtains a reduction of the bias from excessive microwave scattering by precipitation ice for both HUCM bin and the Thompson bulk microphysics schemes for a topographic winter precipitation event associated with an atmospheric river. The Thompson particle size distributions (PSDs) and snow particle density assumption are implemented into the Goddard Satellite Data Simulator Unit (G‐SDSU) and have produced improvements. Despite the greater sophistication of the bin scheme in representing cloud and precipitation processes, the simulation with the Thompson bulk scheme is generally in better agreement with observations for this winter event. The explicitly resolved hydrometeor PSDs in HUCM enable analysis of mass spectra variations in response to changes in microphysics assumptions. Two HUCM sensitivity runs tested the enhancement of snow particle breakup and the influence of ice nuclei (IN) concentration. Higher IN concentration resulted in increased snow mass and broadened the spectrum toward small‐size particles. Modified snow mass spectra and resultant changes in graupel contributed to modifications in scattering and reflectivity simulations. The article demonstrates the bin scheme's capability to provide a new means to improve our understanding of uncertainties in mesoscale weather models and radiative transfer models.

microwave remote sensing↗

NASA NTRS2017

Accuracy/Computation Performance of a New Trilateration Scheme for GPS-Style Localization

We recently introduced a new geometric trilateration (GT) method for GPS-style positioning. Preliminary singlepoint analysis using simplistic error assumptions indicates that the new scheme delivers almost indistinguishable localization accuracy as the traditional Newton-Raphson (NR) approach. Also, the same computation procedure can be used to perform high-accuracy relative positioning between a reference vehicle and an arbitrary number of target vehicles. This scheme has the potential to enable a) new mission concepts in collaborative science, b) in-situ navigation services for human Mars missions, and c) lower cost and faster acquisition of GPS signals for consumer-grade GPS products. The new GT scheme differs from the NR scheme as follows: 1. The new scheme is derived from Pythagoras Theorem, whereas the NR method is based on the principle of linear regression. 2. The NR method uses the absolute locations (xi, yi, zi)’s of the GPS satellites as input to each step of the localization computation. The GT method uses the Directional Cosines Ui’s from Earth’s center to the GPS satellite Si. 3. Both the NR method and the GT method iterate to converge to a localized solution. In each iteration step, multiple matrix operations are performed. The NR method constructs a different matrix in each iterative step, thus requires performing a new set of matrix operations in each step. The GT scheme uses the same matrix in each iteration, thus requiring computing the matrix operations only once for all subsequent iterations. In this paper, we perform an in-depth comparison between the GT scheme and the NR method in terms of a) GPS localization accuracy in the GPS operation environment, b) its sensitivity with respect to systematic errors and random errors, and c) computation load required to converge to a localization solution.

Lee, Charles↗

NASA NTRS2023

Impacts of Estimated Plume Rise on PM 2.5 Exceedance Prediction During Extreme Wildfire Events: A Comparison of Three Schemes (Briggs, Freitas, and Sofiev)

Plume height plays a vital role in wildfire smoke dispersion and the subsequent effects on air quality and human health. In this study, we assess the impact of different plume rise schemes on predicting the dispersion of wildfire air pollution and the exceedances of the National Ambient Air Quality Standards (NAAQS) for fine particulate matter (PM 2.5 ) during the 2020 western United States wildfire season. Three widely used plume rise schemes (Briggs, 1969; Freitas et al., 2007; Sofiev et al., 2012) are compared within the Community Multiscale Air Quality (CMAQ) modeling framework. The plume heights simulated by these schemes are comparable to the aerosol height observed by the Multi-angle Imaging SpectroRadiometer (MISR) and Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observations (CALIPSO). The performance of the simulations with these schemes varies by fire case and weather conditions. On average, simulations with higher plume injection heights predict lower aerosol optical depth (AOD) and surface PM 2.5 concentrations near the source region but higher AOD and PM 2.5 in downwind regions due to the faster spread of the smoke plume once ejected. The 2-month mean AOD difference caused by different plume rise schemes is approximately 20 %–30 % near the source regions and 5 %–10 % in the downwind regions. Thick smoke blocks sunlight and suppresses photochemical reactions in areas with high AOD. The surface PM 2.5 difference reaches 70 % on the West Coast of the USA, and the difference is lower than 15 % in the downwind regions. Moreover, the plume injection height affects pollution exceedance (>35 µg m−3) predictions. Higher plume heights generally produce larger downwind PM 2.5 exceedance areas. The PM 2.5 exceedance areas predicted by the three schemes largely overlap, suggesting that all schemes perform similarly during large wildfire events when the predicted concentrations are well above the exceedance threshold. At the edges of the smoke plumes, however, there are noticeable differences in the PM 2.5 concentration and predicted PM 2.5 exceedance region. For the whole period of study, the difference in the total number of exceedance days could be as large as 20 d in northern California and 4 d in the downwind regions. This disagreement among the PM 2.5 exceedance forecasts may affect key decision-making regarding early warning of extreme air pollution episodes at local levels during large wildfire events.

Yunyao Li↗

NASA NTRS2015

Benefits of a 4th Ice Class in the Simulated Radar Reflectivities of Convective Systems Using a Bulk Microphysics Scheme

Numerous cloud microphysical schemes designed for cloud and mesoscale models are currently in use, ranging from simple bulk to multi-moment, multi-class to explicit bin schemes. This study details the benefits of adding a 4th ice class (hail) to an already improved 3-class ice bulk microphysics scheme developed for the Goddard Cumulus Ensemble model based on Rutledge and Hobbs (1983,1984). Besides the addition and modification of several hail processes from Lin et al. (1983), further modifications were made to the 3-ice processes, including allowing greater ice super saturation and mitigating spurious evaporationsublimation in the saturation adjustment scheme, allowing graupelhail to become snow via vapor growth and hail to become graupel via riming, and the inclusion of a rain evaporation correction and vapor diffusivity factor. The improved 3-ice snowgraupel size-mapping schemes were adjusted to be more stable at higher mixing rations and to increase the aggregation effect for snow. A snow density mapping was also added. The new scheme was applied to an intense continental squall line and a weaker, loosely-organized continental case using three different hail intercepts. Peak simulated reflectivities agree well with radar for both the intense and weaker case and were better than earlier 3-ice versions when using a moderate and large intercept for hail, respectively. Simulated reflectivity distributions versus height were also improved versus radar in both cases compared to earlier 3-ice versions. The bin-based rain evaporation correction affected the squall line case more but did not change the overall agreement in reflectivity distributions.

bulk microphysics schemes↗

NASA NTRS2015

Improving High-Resolution Weather Forecasts using the Weather Research and Forecasting (WRF) Model with an Updated Kain-Fritsch Scheme

Efforts to improve the prediction accuracy of high resolution (1-10 km) surface precipitation distribution and variability are of vital importance to local aspects of air pollution, wet deposition, and regional climate. However, precipitation biases and errors can occur at these spatial scales due to uncertainties in initial meteorological conditions and/or grid-scale cloud microphysics schemes. In particular, it is still unclear to what extent a subgrid-scale convection scheme could be modified to bring in scale-awareness for improving high-resolution short-term precipitation forecasts in the WRF model. To address these issues, we introduced scale-aware parameterized cloud dynamics for high-resolution forecasts by making several changes to the Kain-Fritsch (KF) convective parameterization scheme in the WRF model. These changes include subgrid-scale cloud-radiation interactions, a dynamic adjustment timescale, impacts of cloud updraft mass fluxes on grid-scale vertical velocity, and lifting condensation level-based entrainment methodology that includes scale dependency. A series of 48-hour retrospective forecasts using a combination of three treatments of convection (KF, updated KF, and the use of no cumulus parameterization), two cloud microphysics schemes and two types of initial condition datasets were performed over the U.S. southern Great Plains on 9- and 3-km grid spacings during the summers of 2002 and 2010. Results indicate that (1) the source of initial conditions play a key role in high-resolution precipitation forecasting, and (2) our updated KF scheme greatly alleviates the excessive precipitation at 9-km grid spacing and improves results at 3-km grid spacing as well. Overall, we found that the updated KF scheme incorporated into a high-resolution model does provide better forecasts for precipitation location and intensity.

convective parameterization↗