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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 235 records · Page 13

SSME propellant path leak detection

Initial research established that the occurrence of a leak in the powerhead of the Space Shuttle Main Engine (SSME) is accompanied by a sudden, but sustained, change in intensity in a given region of an image. Based upon this, temporal processing of video images on a frame-by-frame basis has been used to detect leaks within a given field of view. The leak detection algorithm developed in this study consists of a digital highpass filter cascaded with a moving average filter applied at each point in the image field. The absolute value of the output is then averaged over the full frame to produce a single time-varying mean value estimate that is indicative of the intensity and extent of a leak. Recent work has included the processing of an extensive amount of data obtained from NASA MSFC to verify the performance of the leak detection system. Further research is being conducted on applying the leak detection algorithm to anomaly detection in the SSME exhaust by means of three channel color processing as opposed to single channel monochrome processing in the case of the leak detection system.

Smith, L. M.↗

Space Shuttle Main Engine Propellant Path Leak Detection Using Sequential Image Processing

Initial research in this study using theoretical radiation transport models established that the occurrence of a leak is accompanies by a sudden but sustained change in intensity in a given region of an image. In this phase, temporal processing of video images on a frame-by-frame basis was used to detect leaks within a given field of view. The leak detection algorithm developed in this study consists of a digital highpass filter cascaded with a moving average filter. The absolute value of the resulting discrete sequence is then taken and compared to a threshold value to produce the binary leak/no leak decision at each point in the image. Alternatively, averaging over the full frame of the output image produces a single time-varying mean value estimate that is indicative of the intensity and extent of a leak. Laboratory experiments were conducted in which artificially created leaks on a simulated SSME background were produced and recorded from a visible wavelength video camera. This data was processed frame-by-frame over the time interval of interest using an image processor implementation of the leak detection algorithm. In addition, a 20 second video sequence of an actual SSME failure was analyzed using this technique. The resulting output image sequences and plots of the full frame mean value versus time verify the effectiveness of the system.

Smith, L. Montgomery↗

Tests of a Semi-Analytical Case 1 and Gelbstoff Case 2 SeaWiFS Algorithm with a Global Data Set

A semi-analytical algorithm was tested with a total of 733 points of either unpackaged or packaged-pigment data, with corresponding algorithm parameters for each data type. The 'unpackaged' type consisted of data sets that were generally consistent with the Case 1 CZCS algorithm and other well calibrated data sets. The 'packaged' type consisted of data sets apparently containing somewhat more packaged pigments, requiring modification of the absorption parameters of the model consistent with the CalCOFI study area. This resulted in two equally divided data sets. A more thorough scrutiny of these and other data sets using a semianalytical model requires improved knowledge of the phytoplankton and gelbstoff of the specific environment studied. Since the semi-analytical algorithm is dependent upon 4 spectral channels including the 412 nm channel, while most other algorithms are not, a means of testing data sets for consistency was sought. A numerical filter was developed to classify data sets into the above classes. The filter uses reflectance ratios, which can be determined from space. The sensitivity of such numerical filters to measurement resulting from atmospheric correction and sensor noise errors requires further study. The semi-analytical algorithm performed superbly on each of the data sets after classification, resulting in RMS1 errors of 0.107 and 0.121, respectively, for the unpackaged and packaged data-set classes, with little bias and slopes near 1.0. In combination, the RMS1 performance was 0.114. While these numbers appear rather sterling, one must bear in mind what mis-classification does to the results. Using an average or compromise parameterization on the modified global data set yielded an RMS1 error of 0.171, while using the unpackaged parameterization on the global evaluation data set yielded an RMS1 error of 0.284. So, without classification, the algorithm performs better globally using the average parameters than it does using the unpackaged parameters. Finally, the effects of even more extreme pigment packaging must be examined in order to improve algorithm performance at high latitudes. Note, however, that the North Sea and Mississippi River plume studies contributed data to the packaged and unpackaged classess, respectively, with little effect on algorithm performance. This suggests that gelbstoff-rich Case 2 waters do not seriously degrade performance of the semi-analytical algorithm.

Carder, Kendall L.↗

Speed Judgements of Transparent Stimuli

When two moving patterns are combined additively, observers often perceive two transparent surfaces, even when there are no cues supporting this segmentation in a frozen snapshot. We examined the ability of observers to make quantitative judgments about the speed of one of the patterns under these conditions. The component patterns consisted of band-pass filtered random noise presented in a spatial Gaussian contrast envelope, presented for 250 ms. On each trial a standard pattern appeared on one side of the fixation point, while a test pattern appeared on the other. The test pattern moved in the same direction as the standard, but with a speed which varied from trial to trial using a staircase procedure. The subjects' task was to report the side of the fixation point on which faster motion was seen. In some conditions the test stimulus was made to appear transparent by adding a mask pattern. When the mask was stationary, or moved slowly with respect to the test, no significant biases were introduced and discrimination performance was comparable to the no-mask condition (typically 3%). If the mask moved over the test with similar speed, however, the task became much harder, regardless of whether the mask moved opposite or orthogonal to the test. (Some subjects commented on a perceived directional repulsion between tests and orthogonally moving masks.) These results suggest the use of non-directional temporal channels in the performance of the speed discrimination task.

Mulligan, Jeffrey B.↗

Evaluation of the DAO Retrospective Data Assimilation System

We have developed and implemented a retrospective data assimilation system (RDAS) as an upgrade to the operational DAO/Terra data assimilation system. This formulation aims at improving analysis over filter analysis by the dynamically consistent incorporation of observation information past a given analysis time. The current implementation of the RDAS uses the adjoint of the tangent linear model of a simplified version of the Terra general circulation model and extensions to the physical-space statistical analysis system to propagate observation information back in time. The RDAS adopts the same assumptions of the regular data assimilation system, particularly, no explicit propagation of error covariances are involved therefore rendering a procedure that is computationally affordable. In this study, we show results of experiments conducted to investigate the performance of the 6-hour (lag-1) RDAS. Statistical results obtained over one month during a winter season indicate that the RDAS represents considerable improvement over the regular assimilation. Plans for implementation of the RDAS capability in our new finite-volume data assimilation system will also be presented at the time of the conference.

Zhu, Yanqiu↗

Low-Complexity Adaptive Lossless Compression of Hyperspectral Imagery

A low-complexity, adaptive predictive technique for lossless compression of hyperspectral imagery is described. This technique is designed to be suitable for implementation in hardware such as a field programmable gate array (FPGA); such an implementation could be used for high-speed compression of hyperspectral imagery onboard a spacecraft. The predictive step of the technique makes use of the sign algorithm, which is a relative of the least mean square (LMS) algorithm from the field of low-complexity adaptive filtering. The compressed data stream consists of prediction residuals encoded using a method similar to that of the JPEG-LS lossless image compression standard. Compression results are presented for several datasets including some raw Airborne Visible/ Infrared Imaging Spectrometer (AVIRIS) datasets and raw Atmospheric Infrared Sounder (AIRS) datasets. The compression effectiveness obtained with the technique is competitive with that of the best of previously described techniques with similar complexity.

lossless data compression↗

Mass Spectrometer Observing Lunar Operations (MSoLo)

Introduction: In 2019, the National Aeronautics and Space Administration (NASA) announced that it would seek to have humans return to the moon by 2024 in the hopes of establishing a more sustainable lunar presence by 2028. This goal comes with many challenges, one of upmost importance will be to utilize resources that can be found on the moon. Water, which has been identified in the lunar Polar Regions, will be a key resource for in-situ resource utilization (ISRU), as it is capable of being processed for vehicular fuel, as well as life support systems materials such as oxygen. Upcoming Commercial Lunar Payload Services (CLPS) missions will be critical for these resource assessments. Methods: A modified commercial off-the-shelf (COTS) mass spectrometer developed at Kennedy Space Center known as MSolo, consisting of a quadrupole mass filter and space rated electronics undergoes testing and modifications in order to study operational parameters to unconventional approaches needed in flight situations. In general, MSolo operates in the 0-100 m/z range with the ability to detect with a faraday cup (FC) or an electron multiplier (EM) for enhanced detection. A crossbeam (XB) ionization source is used. Preliminary Data: Prior to construction, little information was available on how the MSolo system would perform at lunar like environments, factors such as temperatures (possible fluctuations from 70 to -45 °C), vibrations from launch and their side effects, the general ability to operate while the entire system (hardware and electronic components) were in a vacuum environment, were factors that while know to flight instruments, were something new to a modified COTS system. As components start to warm up, temperature becomes a key factor (ie. heat can no longer escape the electronics as no atmosphere is present), therefore it becomes crucial to find new ways to maintain stable signals and keep the instrument tuned. Calibration itself becomes an important parameter that needs to be performed while maintaining all flight like characteristics. Even the structure itself of MSolo’s sensor needed to be changed to survive the verification parameters needed to be approved for flight. Most important, all the modifications made to the COTS system have to keep the instrument working at the same specifications of the standard commercial systems. Novel Aspect: Results gathered provide key parameters that will assist to the unconventional mass spectrometry approaches of the upcoming CLPS missions to which MSolo has been selected to.

MSolo↗

Deep Space navigation for the BioSentinel spacecraft science orbit

BioSentinel is an astrobiology small spacecraft mission. The payload consists of two parts, the first has optical and microfluidics sensors, and the second is a Linear Energy Transfer spectrometer that has the objective to measure deep space radiation from events such as coronal mass ejections. The goal of the mission is to observe potential DNA damage due to the radiation in heliocentric space on the living organism Saccharomyces cerevisiae, which is a budding yeast. Two types of this living organism are included in the payload. The first is a natural type that is more radiation tolerant, while the second is a mutant strain that has a deficiency in a gene that allows DNA repair once damage occurs. The impact caused by the radiation on the DNA is compared to an identical sample aboard the International Space Station, as well as another identical sample at a laboratory on the ground. The BioSentinel mission consists of a 6U CubeSat currently ,as of January 2024, active in heliocentric orbit. The spacecraft was launched aboard the first SLS flight as part of the Artemis-I campaign in November 2022. After successful deployment from the launch vehicle, it performed a lunar flyby with an altitude of 406 km. The delta-V imparted by the flyby provided the necessary energy to achieve a heliocentric orbit, in an Earth-trailing pattern. The navigation analysis consisted of a Kalman-filter that utilized data from the Deep Space Network and the ESA Estrack network. All those antennas were needed since the Artemis-1 campaign included the deployment of several other cubesats, therefore the scheduling process required more antenna assets than usual due to simultaneous demands from various missions. The processed tracking data was later also refined with a smoother in order to obtain a more accurate solution. The type of tracking data included TCP, Sequential Range, Doppler and Range formats. The solar radiation pressure coefficient, as well as the delta-V from the deployment and the flyby were modeled to obtain suitable solutions that could decrease the position and velocity uncertainties at several steps along the mission concept of operations. The final product each time resulted in updated ephemeris files that were used by the mission and the antenna networks as the mission progressed. Once in the final science orbit, the utilized antennas are only from the DSN network and the data format is bounded to just TCP. Regular orbit determination is performed, every two weeks. The spacecraft is in a nominal well-known orbit, performing regular operations. This paper includes an analysis of the final science orbit, the techniques and procedures utilized to perform orbit determination and a description of the overall navigation campaign produced during the mission and, more specifically, during the final science operations in Deep Space.

BioSentinel↗

Failure detection by pilots during automatic landing: Models and experiments

A model of the pilot as a monitor of instrument failures during automatic landing is proposed. The failure detection model consists of two stages: a linear estimator (Kalman Filter) and a decision mechanism which is based on sequential analysis. The filter equations are derived from a simplified version of the linearized dynamics of the airplane and the control loop. The perceptual observation noise is modelled to include the effects of the partition of attention among the several instruments. The final result is a simple model consisting of a high pass filter to produce the observation residuals, and a decision function which is a pure integration of the residuals minus a bias term. The dynamics of a Boeing 707 were used to simulate the fully coupled final approach in a fixed base simulator which also included failures in the airspeed, glideslope, and localizer indicators. Subjects monitored the approaches and detected the failures; their performance was compared with the predictions of the model with good agreement between the experimental data and the model.

Gai, E. G.↗

Miniature L-Band Radar Transceiver

A miniature L-band transceiver that operates at a carrier frequency of 1.25 GHz has been developed as part of a generic radar electronics module (REM) that would constitute one unit in an array of many identical units in a very-large-aperture phased-array antenna. NASA and the Department of Defense are considering the deployment of such antennas in outer space; the underlying principles of operation, and some of those of design, also are applicable on Earth. The large dimensions of the antennas make it advantageous to distribute radio-frequency electronic circuitry into elements of the arrays. The design of the REM is intended to implement the distribution. The design also reflects a requirement to minimize the size and weight of the circuitry in order to minimize the weight of any such antenna. Other requirements include making the transceiver robust and radiation-hard and minimizing power demand. Figure 1 depicts the functional blocks of the REM, including the L-band transceiver. The key functions of the REM include signal generation, frequency translation, amplification, detection, handling of data, and radar control and timing. An arbitrary-waveform generator that includes logic circuitry and a digital-to-analog converter (DAC) generates a linear-frequency-modulation chirp waveform. A frequency synthesizer produces local-oscillator signals used for frequency conversion and clock signals for the arbitrary-waveform generator, for a digitizer [that is, an analog-to-digital converter (ADC)], and for a control and timing unit. Digital functions include command, timing, telemetry, filtering, and high-rate framing and serialization of data for a high-speed scientific-data interface. The aforementioned digital implementation of filtering is a key feature of the REM architecture. Digital filters, in contradistinction to analog ones, provide consistent and temperature-independent performance, which is particularly important when REMs are distributed throughout a large array. Digital filtering also enables selection among multiple filter parameters as required for different radar operating modes. After digital filtering, data are decimated appropriately in order to minimize the data rate out of an antenna panel. The L-band transceiver (see Figure 2) includes a radio-frequency (RF)-to-baseband down-converter chain and an intermediate- frequency (IF)-to-RF up-converter chain. Transmit/receive (T/R) switches enable the use of a single feed to the antenna for both transmission and reception. The T/R switches also afford a built-in test capability by enabling injection of a calibration signal into the receiver chain. In order of decreasing priority, components of the transceiver were selected according to requirements of radiation hardness, then compactness, then low power. All of the RF components are radiation-hard. The noise figure (NF) was optimized to the extent that (1) a low-noise amplifier (LNA) (characterized by NF < 2 dB) was selected but (2) the receiver front-end T/R switches were selected for a high degree of isolation and acceptably low loss, regardless of the requirement to minimize noise.

McWatters, Dalia↗

Bayesian investigation of isochrone consistency using the old open cluster NGC 188

This paper provides a detailed comparison of the differences in parameters derived for a star cluster from its color–magnitude diagrams (CMDs) depending on the filters and models used. We examine the consistency and reliability of fitting three widely used stellar evolution models to 15 combinations of optical and near-IR photometry for the old open cluster NGC 188. The optical filter response curves match those of theoretical systems and are thus not the source of fit inconsistencies. NGC 188 is ideally suited to this study thanks to a wide variety of high-quality photometry and available proper motions and radial velocities that enable us to remove non-cluster members and many binaries. Our Bayesian fitting technique yields inferred values of age, metallicity, distance modulus, and absorption as a function of the photometric band combinations and stellar models. We show that the historically favored three-band combinations of UBV and VRI can be meaningfully inconsistent with each other and with longer baseline data sets such as UBVRIJHK{sub S}. Differences among model sets can also be substantial. For instance, fitting Yi et al. (2001) and Dotter et al. (2008) models to UBVRIJHK{sub S} photometry for NGC 188 yields the following cluster parameters: age = (5.78 ± 0.03, 6.45 ± 0.04) Gyr, [Fe/H] = (+0.125 ± 0.003, −0.077 ± 0.003) dex, (m−M){sub V} = (11.441 ± 0.007, 11.525 ± 0.005) mag, and A{sub V} = (0.162 ± 0.003, 0.236 ± 0.003) mag, respectively. Within the formal fitting errors, these two fits are substantially and statistically different. Such differences among fits using different filters and models are a cautionary tale regarding our current ability to fit star cluster CMDs. Additional modeling of this kind, with more models and star clusters, and future Gaia parallaxes are critical for isolating and quantifying the most relevant uncertainties in stellar evolutionary models.

79 ASTRONOMY AND ASTROPHYSICS↗

Miniature spectrally selective dosimeter

A miniature spectrally selective dosimeter capable of measuring selected bandwidths of radiation exposure on small mobile areas is described. This is achieved by the combination of photovoltaic detectors, electrochemical integrators (E-cells) and filters in a small compact case which can be easily attached in close proximity to and substantially parallel to the surface being measured. In one embodiment two photovoltaic detectors, two E-cells, and three filters are packaged in a small case with attaching means consisting of a safety pin. In another embodiment, two detectors, one E-cell, three filters are packaged in a small case with attaching means consisting of a clip to clip over a side piece of an eye glass frame.

Adams, R. R.↗

Failure detection by pilots during automatic landing - Models and experiments

A model is proposed to describe the pilot as a monitor of automatic landing systems. The failures treated are equivalent to the addition of a dynamic change in the mean of the observation process. The failure detection model of the pilot consists of two stages: a linear estimator (Kalman filter) and a decision mechanism based on sequential analysis. The filter equations are derived from a simplified version of the linearized dynamics of the airplane and the control loop. The perceptual observation noise is modified to include the effects of allocation of attention among the several instruments. The final result is a simple model consisting of a high-pass filter to produce the observation residuals and a decision function which is a pure integration of the residuals minus a bias term. The dynamics of a Boeing 707 were used to simulate the fully coupled final approach in a fixed-base simulator. Observers monitored the approaches and detected the failures; their performance was compared with the predictions of the model.

Gai, E. G.↗

A Multi-Model Adaptive Kalman Filtering Approach to Power System Dynamic State Estimation

Accurate information about dynamic states (such as rotor angle and speed of a synchronous machine) is important for monitoring and controlling power system rotor-angle stability. In this paper, a multi-model adaptive Kalman filtering (MMAKF) approach is proposed to accurately and robustly estimate power system dynamic states. This approach consists of three major steps: (i) multiple Kalman filtering approaches, i.e., the extended Kalman filter (EKF), unscented Kalman filter (UKF), ensemble Kalman filter (EnKF), and cubature Kalman filter (CKF), are run concurrently in parallel to estimate the dynamic states of a synchronous generator using phasor measurement unit data; (ii) probability indexes, which quantify the likelihood of each estimation model, are determined at each time step using hypothesis testing based on the measurement innovation; (iii) the a posteriori estimate of states is obtained using the best-fix approach. The two-area four-machine system is used to evaluate the effectiveness of the proposed MMAKF approach. It is shown through the Monte-Carlo method that the estimation accuracy and robustness of the proposed approach is better than those from any individual filtering algorithm.

multi-model adaptive Kalman Filtering, Power Syste↗

Multiscale assessment of North American terrestrial carbon balance

Abstract. Comparisons of carbon uptake estimates from bottom-up terrestrial biosphere models (TBMs) to top-down atmospheric inversions help assess how well we understand carbon dioxide (CO2) exchange between the atmosphere and terrestrial biosphere. Previous comparisons have shown varying levels of agreement between bottom-up and top-down approaches, but they have almost exclusively focused on large, aggregated scales (e.g., global or continental), providing limited insights into reasons for the mismatches. Here we explore how consistency, defined as the spread in net ecosystem exchange (NEE) estimates within an ensemble of TBMs or inversions, varies with at finer spatial scales ranging from 1∘×1∘ to the continent of North America. We also evaluate how well consistency informs accuracy in overall NEE estimates by filtering models based on their agreement with the variability, magnitude, and seasonality in observed atmospheric CO2 drawdowns or enhancements. We find that TBMs produce more consistent estimates of NEE for most regions and at most scales relative to inversions. Filtering models using atmospheric CO2 metrics causes ensemble spread to decrease substantially for TBMs, but not for inversions. This suggests that ensemble spread is likely not a reliable measure of the uncertainty associated with the North American carbon balance at any spatial scale. Promisingly, applying atmospheric CO2 metrics leads to a set of models with converging flux estimates across TBMs and inversions. Overall, we show that multiscale assessment of the agreement between bottom-up and top-down NEE estimates, aided by regional-scale observational constraints is a promising path towards identifying fine-scale sources of uncertainty and improving both ensemble consistency and accuracy. These findings help refine our understanding of biospheric carbon balance, particularly at scales relevant for informing regional carbon-climate feedbacks.

54 ENVIRONMENTAL SCIENCES↗

Development of an Indexing Media Filtration System for Long Duration Space Missions

The effective maintenance of air quality aboard spacecraft cabins will be vital to future human exploration missions. A key component will be the air cleaning filtration system which will need to remove a broad size range of particles including skin flakes, hair and clothing fibers, other biological matter, and particulate matter derived from material and equipment wear. In addition, during surface missions any extraterrestrial planetary dust, including dust generated by near-by ISRU equipment, which is tracked into the habitat will also need to be managed by the filtration system inside the pressurized habitat compartments. An indexing media filter system is being developed to meet the demand for long-duration missions that will result in dramatic increases in filter service life and loading capacity, and will require minimal crew involvement. These features may also benefit other closed systems, such as submarines, and remote location terrestrial installations where servicing and replacement of filter units is not practical. The filtration system consists of three stages: an inertial impactor stage, an indexing media stage, and a high-efficiency filter stage, packaged in a stacked modular cartridge configuration. Each stage will target a specific range of particle sizes that optimize the filtration and regeneration performance of the system. An 1/8th scale and full-scale prototype of the filter system have been fabricated and have been tested in the laboratory and reduced gravity environments that simulate conditions on spacecrafts, landers and habitats. Results from recent laboratory and reducegravity flight tests data will be presented.

Filtration↗

Results from Evaluation of Proposed ASME AG-1 Section FI Metal Media Filters - 13063

High efficiency particulate air (HEPA) filtration technology is commonly used in Department of Energy (DOE) facilities that require control of radioactive particulate matter (PM) emissions due to treatment or management of radioactive materials. Although HEPA technology typically makes use of glass fiber media, metal and ceramic media filters are also capable of filtering efficiencies beyond the required 99.97%. Sintered metal fiber filters are good candidates for use in DOE facilities due to their resistance to corrosive environments and resilience at high temperature and elevated levels of relative humidity. Their strength can protect them from high differential pressure or pressure spikes and allow for back pulse cleaning, extending filter lifetime. Use of these filters has the potential to reduce the cost of filtration in DOE facilities due to life cycle cost savings. ASME AG-1 section FI has not been approved due to a lack of protocols and performance criteria for qualifying section FI filters. The Institute for Clean Energy Technology (ICET) with the aid of the FI project team has developed a Section FI test stand and test plan capable of assisting in the qualification ASME AG-1 section FI filters. Testing done at ICET using the FI test stand evaluates resistance to rated air flow, test aerosol penetration and resistance to heated air of the section FI filters. Data collected during this testing consists of temperature, relative humidity, differential pressure, flow rate, upstream particle concentration, and downstream particle concentration. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Adaptive Numerical Dissipative Control in High Order Schemes for Multi-D Non-Ideal MHD

The goal is to extend our adaptive numerical dissipation control in high order filter schemes and our new divergence-free methods for ideal MHD to non-ideal MHD that include viscosity and resistivity. The key idea consists of automatic detection of different flow features as distinct sensors to signal the appropriate type and amount of numerical dissipation/filter where needed and leave the rest of the region free of numerical dissipation contamination. These scheme-independent detectors are capable of distinguishing shocks/shears, flame sheets, turbulent fluctuations and spurious high-frequency oscillations. The detection algorithm is based on an artificial compression method (ACM) (for shocks/shears), and redundant multi-resolution wavelets (WAV) (for the above types of flow feature). These filter approaches also provide a natural and efficient way for the minimization of Div(B) numerical error. The filter scheme consists of spatially sixth order or higher non-dissipative spatial difference operators as the base scheme for the inviscid flux derivatives. If necessary, a small amount of high order linear dissipation is used to remove spurious high frequency oscillations. For example, an eighth-order centered linear dissipation (AD8) might be included in conjunction with a spatially sixth-order base scheme. The inviscid difference operator is applied twice for the viscous flux derivatives. After the completion of a full time step of the base scheme step, the solution is adaptively filtered by the product of a 'flow detector' and the 'nonlinear dissipative portion' of a high-resolution shock-capturing scheme. In addition, the scheme independent wavelet flow detector can be used in conjunction with spatially compact, spectral or spectral element type of base schemes. The ACM and wavelet filter schemes using the dissipative portion of a second-order shock-capturing scheme with sixth-order spatial central base scheme for both the inviscid and viscous MHD flux derivatives and a fourth-order Runge-Kutta method are denoted.

Yee, H. C.↗