Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “collocation”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 1,081 records · Page 60

Distributed Relaxation for Conservative Discretizations

A multigrid method is defined as having textbook multigrid efficiency (TME) if the solutions to the governing system of equations are attained in a computational work that is a small (less than 10) multiple of the operation count in one target-grid residual evaluation. The way to achieve this efficiency is the distributed relaxation approach. TME solvers employing distributed relaxation have already been demonstrated for nonconservative formulations of high-Reynolds-number viscous incompressible and subsonic compressible flow regimes. The purpose of this paper is to provide foundations for applications of distributed relaxation to conservative discretizations. A direct correspondence between the primitive variable interpolations for calculating fluxes in conservative finite-volume discretizations and stencils of the discretized derivatives in the nonconservative formulation has been established. Based on this correspondence, one can arrive at a conservative discretization which is very efficiently solved with a nonconservative relaxation scheme and this is demonstrated for conservative discretization of the quasi one-dimensional Euler equations. Formulations for both staggered and collocated grid arrangements are considered and extensions of the general procedure to multiple dimensions are discussed.

Diskin, Boris↗

Arctic Stratus Cloud Properties and Their Effect on the Surface Radiation Budget: Selected Cases from FIRE ACE

To study Arctic stratus cloud properties and their effect on the surface radiation balance during the spring transition season, analyses are performed using data taken during three cloudy and two clear days in May 1998 as part of the First ISCCP Regional Experiment (FIRE) Arctic Cloud Experiment (ACE). Radiative transfer models are used in conjunction with surface- and satellite-based measurements to retrieve the layer-averaged microphysical and shortwave radiative properties. The surface-retrieved cloud properties in Cases 1 and 2 agree well with the in situ and satellite retrievals. Discrepancies in Case 3 are due to spatial mismatches between the aircraft and the surface measurements in a highly variable cloud field. Also, the vertical structure in the cloud layer is not fully characterized by the aircraft measurements. Satellite data are critical for understanding some of the observed discrepancies. The satellite-derived particle sizes agree well with the coincident surface retrievals and with the aircraft data when they were collocated. Optical depths derived from visible-channel data over snow backgrounds were overestimated in all three cases, suggesting that methods currently used in satellite cloud climatologies derive optical depths that are too large. Use of a near-infrared channel with a solar infrared channel to simultaneously derive optical depth and particle size appears to alleviate this overestimation problem. Further study of the optical depth retrieval is needed. The surface-based radiometer data reveal that the Arctic stratus clouds produce a net warming of 20 W m(exp -2) in the surface layer during the transition season suggesting that these clouds may accelerate the spring time melting of the ice pack. This surface warming contrasts with the net cooling at the top of the atmosphere (TOA) during the same period. All analysis of the complete FIRE ACE data sets will be valuable for understanding the role of clouds during the entire melting and refreezing process that occurs annually in the Arctic.

Doug, Xiquan↗

Airborne Aerosol Closure Studies During PRIDE

The Puerto Rico Dust Experiment (PRIDE) was conducted during June/July of 2000 to study the properties of Saharan dust aerosols transported across the Atlantic Ocean to the Caribbean Islands. During PRIDE, the NASA Ames Research Center six-channel (380 - 1020 nm) airborne autotracking sunphotometer (AATS-6) was operated aboard a Piper Navajo airplane alongside a suite of in situ aerosol instruments. The in situ aerosol instrumentation relevant to this paper included a Forward Scattering Spectrometer Probe (FSSP-100) and a Passive Cavity Aerosol Spectrometer Probe (PCASP), covering the radius range of approx. 0.05 to 10 microns. The simultaneous and collocated measurement of multi-spectral aerosol optical depth and in situ particle size distribution data permits a variety of closure studies. For example, vertical profiles of aerosol optical depth obtained during local aircraft ascents and descents can be differentiated with respect to altitude and compared to extinction profiles calculated using the in situ particle size distribution data (and reasonable estimates of the aerosol index of refraction). Additionally, aerosol extinction (optical depth) spectra can be inverted to retrieve estimates of the particle size distributions, which can be compared directly to the in situ size distributions. In this paper we will report on such closure studies using data from a select number of vertical profiles at Cabras Island, Puerto Rico, including measurements in distinct Saharan Dust Layers. Preliminary results show good agreement to within 30% between mid-visible aerosol extinction derived from the AATS-6 optical depth profiles and extinction profiles forward calculated using 60s-average in situ particle size distributions and standard Saharan dust aerosol refractive indices published in the literature. In agreement with tendencies observed in previous studies, our initial results show an underestimate of aerosol extinction calculated based on the in situ size distributions relative to the extinction obtained from the sunphotometer measurements. However, a more extensive analysis of all available AATS-6 and in situ size distribution data is necessary to ascertain whether the preliminary results regarding the degree of extinction closure is representative of the entire range of dust conditions encountered in PRIDE. Finally, we will compare the spectral extinction measurements obtained in PRIDE to similar data obtained in Saharan dust layers encountered above the Canary Islands during ACE-2 (Aerosol Characterization Experiment) in July 1997. Thus, the evolution of Saharan dust spectral properties during its transport across the Atlantic can be investigated, provided the dust origin and microphysical properties are found to be comparable.

Redemann, Jens↗

Comparison of Shortwave Cloud Radiative Forcing Derived from ARM SGP Surface and GOES-8 Satellite Measurements During ARESE I and ARESE II

One of the objectives of the ARM Enhanced Shortwave Experiment (ARESE) is to investigate the absorption of solar radiation by clouds over the ARM Southern Great Plains central facility. A variety of techniques employing various combinations Of Surface, aircraft, and satellite data have been used to estimate the absorption empirically. During ARESE-I conducted during fall 1995, conflicting results were produced from different analyses of the combined datasets leading to the need for a more controlled experiment. ARESE-II was conducted during spring 2000. Improved calibrations, different sampling strategies, and broadband satellite data were all available to minimize some of the sources of uncertainty in the data. In this paper, cloud absorption or its parametric surrogates (e.g., Cess et al. 1995) are derived from collocated and coincident surface and satellite radiometer data from both ARESE-I and ARESE-II using the latest satellite and surface instrument calibrations.

Rapp, A. D.↗

Vertical Profiles of Latent Heating in TRMM: Validation and Assimilation in the GEOS Data Assimilation System

I have derived the vertical profiles of apparent heating Q and Q2 by using 3-hourly balloon sounding data from the ARM SGP sounding array for three IOPs in 2000. These IOPs cover the periods from 3/1 to 3/22, from 9/25 to 10/8, and from 11/27 to 12/22. These heating profiles will be collocated with the TRMM heating profiles for validation studies once the TRMM profiles become available to the investigators. I have also produced the objective analyses of Q1, Q2 and forcing fields for the international GCSS Case 3 Intercomparison project. The GSFC CRM participated in study, based on which TRMM heating profiles are derived. I have also studied to assimilate the vertical heating profile by constraining the cloud-base mass flux in the cumulus convection scheme using the CCM3. I first derive the vertical heating profile for each convective plume of unit cloud-base mass flux. The observed heating profile form ARM is then de-convoluted to derive the cloud base mass fluxes of all individual plumes. These fluxes are compared with those derived from the quasi-equilibrium hypothesis. They are shown to improve many other aspects of the model behavior.

Zhang, Ming-Hua↗

SeaWinds Scatterometer on QuikSCAT Mission and the Emerging Land and Ocean Applications

Spaceborne scatterometers are active microwave radar instruments designed to acquire near-simultaneous, spatially collocated measurements of the normalized radar backscattering cross section (sigma0) of the global surface from several azimuth and/or incidence angles. The primary objective of the scatterometer mission is to measure the near-surface wind speed and direction over the global ocean using sigma0 measurements together with a wind geophysical model function. However, since sigma0 measurements are collected globally all the time, sigma0 data can also be used for global land and ice applications. In this paper, we will first present the objectives of the QSCAT mission, the instrument design, and the unique features of the Ku-band scatterometer currently in operation, called SeaWinds on QuikSCAT (QSCAT). We will then present some emerging land and ocean applications of the QSCAT data, which include (1) global snow detection and monitoring, (2) melt region mapping on the Greenland ice sheet, (3) Monsoon flood detection and monitoring, (4) soil wetness application at large scale, and (5) hurricane monitoring and tracking.

Tsai, W.-Y.↗

The SMART Ground-based Remote Sensing for Terra/MODIS Validation

A ground-based remote sensing system - SMART (Surface Measurements for Atmospheric Radiative Transfer) - was deployed during both the SAFARI-2000 and the ARREX-1999 dry season campaigns. The measurement site is the Skukuza airport. The operation period for 1999 is from August 16 to September 10. The main instruments include shortwave (approximately 0.28-2.8 micrometers) and longwave (approximately 4-50 micrometers) broadband radiometers, a shadow-band radiometer, a micro-pulse lidar, and a microwave radiometer. We also did some measurements of solar spectral flux by using an ASD spectrometer. The operation period for 2000 is from August 15 to September 22. This time we added a few new features to the SMART system: a solar tracker for direct and diffuse components of solar fluxes; the scanning capability to the microwave radiometer; a whole sky camera for documenting the sky conditions every minute; and a mini-weather station for atmospheric pressure, temperature, humidity, wind speed/direction. A surface SSFR (Solar Spectral Flux Radiometer) from NASA Ames also joined us for the measurements. This is a unique data set with reasonably long observational period and high accuracy. The data show good correlation with the local weather patterns. We also see diurnal change and some special events, such as fierce fires nearby. To quantify the surface radiative forcing of biomass burning aerosols, many pyranometers, pyrgeometers, and pyrheliometers measure the global, direct, and diffuse irradiance at the surface. These fluxes combining with the collocated optical thickness retrievals from sun photometer (or shadow-band radiometer), the solar radiative forcing, proportional to delta F/delta tau, can be investigated. Integrated with measurements of other instruments at the site, these data sets will serve as "ground truth" for the satellite measurements and modeling.

Tsay, Si-Chee↗

On the Two-Dimensionalization of Homogeneous Rotating Turbulence

Large-eddy simulation of the incompressible Navier-Stokes equations has been used to examine the long-time development of initially isotropic turbulence subjected to solid-body rotation. The simulations were carried out using a pseudo-spectral method with 128 x 128 x 512 collocation points in a computational domain that is four times larger along the rotation axis than in the other directions; subgrid-scale motions were parameterized using a spectral eddy viscosity model modified for system rotation. Simulation results show that the correlation length along the rotation am's of velocities orthogonal to the rotation vector exhibits rapid growth while the integral length-scale of velocities aligned with the rotation axis is relatively unaffected by rotation. Examination of the energy spectrum of two-dimensional, two-component motions indicates the presence of an inverse cascade of energy. System rotation also causes an alignment of vorticity along the rotation axis with relatively stronger cyclonic vorticity than anticyclonic. The onset of anisotropic effects are well characterized by Rossby numbers defined in terms of both macroscopic and microscopic quantities.

Squires, K. D.↗

A Multiyear Dataset of SSM/I-Derived Global Ocean Surface Turbulent Fluxes

The surface turbulent fluxes of momentum, latent heat, and sensible heat over global oceans are essential to weather, climate and ocean problems. Evaporation is a key component of the hydrological cycle and the surface heat budget, while the wind stress is the major forcing for driving the oceanic circulation. The global air-sea fluxes of momentum, latent and sensible heat, radiation, and freshwater (precipitation-evaporation) are the forcing for driving oceanic circulation and, hence, are essential for understanding the general circulation of global oceans. The global air-sea fluxes are required for driving ocean models and validating coupled ocean-atmosphere global models. We have produced a 7.5-year (July 1987-December 1994) dataset of daily surface turbulent fluxes over the global oceans from the Special Sensor microwave/Imager (SSM/I) data. Daily turbulent fluxes were derived from daily data of SSM/I surface winds and specific humidity, National Centers for Environmental Prediction (NCEP) sea surface temperatures, and European Centre for Medium-Range Weather Forecasts (ECMWF) air-sea temperature differences, using a stability-dependent bulk scheme. The retrieved instantaneous surface air humidity (with a 25-km resolution) validated well with that of the collocated radiosonde observations over the global oceans. Furthermore, the retrieved daily wind stresses and latent heat fluxes were found to agree well with that of the in situ measurements (IMET buoy, RV Moana Wave, and RV Wecoma) in the western Pacific warm pool during the TOGA COARE intensive observing period (November 1992-February 1993). The global distributions of 1988-94 seasonal-mean turbulent fluxes will be presented. In addition, the global distributions of 1990-93 annual-means turbulent fluxes and input variables will be compared with those of UWM/COADS covering the same period. The latter is based on the COADS (comprehensive ocean-atmosphere data set) and is recognized to be one of the best climatological analyses of fluxes derived from ship observations.

Chou, Shu-Hsien↗

Combining TOPEX and SeaWinds Data to Refine Models for Ocean Surface Emissivity: Wind Vector Signatures at 18, 21 and 37 GHz

TOPEX Microwave Radiometer (TMR) brightness temperature observations at 18, 21, and 37 GHz have been collocated with near-simultaneous SeaWinds wind vector data as well as with a monthly SST climatological product. The combined data set allows us to study the dependence of ocean surface emissivity (at each frequency) upon both wind speed. Results show clear two-branch wind speed dependence; weak and linear below 6 m/s with an abrupt increase in sensitivity above that point. The analysis also shows that the zenith-directed ocean surface emissivity is polarization dependent above wind speeds of 5-6 m/s with an azimuthal variation related to the wind direction. This last result accords with recent polarimetric radiometer observations collected from aircraft. Implications of these observations to water vapor retrieval algorithms, nadir-viewing polarimetry, and ocean emission modeling will be discussed.

Vandemark, D.↗

Thermal Electron Contributions to Current-Driven Instabilities: SCIFER Observations in the 1400-km Cleft Ion Fountain and Their Implications to Thermal Ion Energization

SCIFER TECHS observations of the variations in the thermal electron distribution in the 1400-km altitude cleft are associated with periods of intense ion heating and field-aligned currents. Energization of the thermal ion plasma in the mid-altitude cleft occurs within density cavities accompanied by enhanced thermal electron temperatures, large field-aligned thermal electron plasma flows and broadband low-frequency electric fields. Variations in the thermal electron contribution to field-aligned current densities indicate small scale (approximately 100's m) filamentary structure embedded within the ion energization periods. TECHS observations of the field-aligned drift velocities and temperatures of the thermal electron distribution are presented to evaluate the critical velocity thresholds necessary for the generation of electrostatic ion cyclotron and ion acoustic instabilities. This analysis suggests that, during periods of thermal ion energization, sufficient drift exists in the thermal electron distribution to excite the electrostatic ion cyclotron instability. In addition, brief periods exist within the same interval where the drift of the thermal electron distribution is sufficient to marginally excite the ion acoustic instability. In addition, the presence an enhancement in Langmuir emission at the plasma frequency at the center of the ion energization region, accompanied by the emission's second-harmonic, and collocated with observations of high-frequency electric field solitary structures suggest the presence of electron beam driven decay of Langmuir waves to ion acoustic modes as an additional free energy source for ion energization.

Adrian, Mark L.↗

On the Conservation and Convergence to Weak Solutions of Global Schemes

In this paper we discuss the issue of conservation and convergence to weak solutions of several global schemes, including the commonly used compact schemes and spectral collocation schemes, for solving hyperbolic conservation laws. It is shown that such schemes, if convergent boundedly almost everywhere, will converge to weak solutions. The results are extensions of the classical Lax-Wendroff theorem concerning conservative schemes.

Carpenter, Mark H.↗

Observations and Parameterizations of Particle Size Distributions in Deep Tropical Cirrus and Stratiform Precipitation Clouds: Results from In-Situ Observations in TRMM Field Campaigns

In this study, we report on the evolution of particle size distributions (PSDs) and habits as measured during slow, Lagrangian-type spiral descents through deep subtropical and tropical cloud layers in Florida, Brazil, and Kwajalein, Marshall Islands, most of which were precipitating. The objective of the flight patterns was to learn more about how the PSDs evolved in the vertical and to obtain information of the vertical structure of microphysical properties. New instrumentation yielding better information on the concentrations of particles in the size (D) range between 0.2 and 2 cm, as well as improved particle imagery, produced more comprehensive observations for tropical stratiform precipitation regions and anvils than have been available previously. Collocated radar observations provided additional information on the vertical structure of the cloud layers sampled. Most of the spirals began at cloud top, with temperatures (T) as low as -50 C, and ended at cloud base or below the melting layer (ML). The PSDs broadened from cloud top towards cloud base, with the largest particles increasing in size from several millimeters at cloud top to one centimeter or larger towards cloud base. Some continued growth was noted in the upper part of the ML. Concentrations of particles less than 1 mm in size decreased with decreasing height. The result was a consistent change in the PSDs in the vertical. Similarly, systematic changes in the size dependence of the particle cross-sectional area was noted with decreasing height. Aggregation-as ascertained from both the changes in the PSDs and evolution of particle habits as observed in high detail with the cloud particle imager (CPI) probe-was responsible for these trends. The PSDs were generally well-represented by gamma distributions of the form N = N0 gamma D microns e- lambda gamma D that were fitted to the PSDs over 1-km horizontal intervals throughout the spirals. The intercept (N0 gamma), slope (lambda gamma), and dispersion (microns) values were derived for each PSD. Exponential curves (N = N0e- lambdaD; micron = 0) were also fitted to the distributions. The lambda gamma values for given spirals varied systematically with temperature as did the values of lambda (exponential), and the data generally conformed to values found in previous studies involving exponential fits to size distributions in mid-latitude frontal and cirrus layers. Considerable variability often noted in the PSD properties during the loops of individual spirals was manifested primarily in large changes in N0 gamma and N0, but micron, lambda gamma and lambda remained fairly stable. Temperature is not found to be the sole factor controlling lambda gamma or lambda but is a primary one. Direct relationships were found between lambda gamma and N0 gamma or lambda gamma and micron for the gamma distributions and lambda and N0 for the exponential. The latter relationship was not found as distinctly in earlier studies; observed PSDs in this study had better fidelity with less scatter. The micron values changed monotonically with T over the range of temperatures and were directly related to N0 gamma or lambda gamma, thereby reducing the number of variables in the PSD functional equation to two. In the upper part of the ML, N0 and lambda continued to decrease, and in the lower part these values began to increase as the largest particles melted. We developed general expressions relating various bulk microphysical, radar, and radiative transfer-related variables to N0 gamma and lambda gamma, useful for both tropical and mid-latitude clouds. These relationships facilitate the specification of a number of bulk properties in cloud and climate models. The results presented in this paper apply best to temperatures between 0 and -40 C, for which the measured radar reflectivities fall in the range of 0 to 25 dBZe.

Heymsfield, Andrew J.↗

Decoupling the Role of Particle Inertia and Gravity on Particle Dispersion

Particle dispersion and the influence that particle momentum exchange has on the properties of a turbulent carrier flow in micro-gravity environments challenge present understanding and predictive schemes. The objective of this effort has been to develop and assess high-fidelity simulation tools for predicting particle transport within micro-gravity environments suspended in turbulent flows. The computational technique is based on Direct Numerical Simulation (DNS) of the incompressible Navier-Stokes equations. The particular focus of the present work is on the class of dilute flows in which particle volume fractions and inter-particle collisions are negligible. Particle motion is assumed to be governed by drag with particle relaxation times ranging from the Kolmogorov scale to the Eulerian timescale of the turbulence and particle mass loadings up to one. The velocity field was made statistically stationary by forcing the low wavenumbers of the flow. The calculations were performed using 96(exp 3) collocation points and the Taylor-scale Reynolds number for the stationary flow was 62. The effect of particles on the turbulence was included in the Navier-Stokes equations using the point-force approximation in which 96(exp 3) particles were used in the calculations. DNS results show that particles increasingly dissipate fluid kinetic energy with increased loading, with the reduction in kinetic energy being relatively independent of the particle relaxation time. Viscous dissipation in the fluid decreases with increased loading and is larger for particles with smaller relaxation times. Fluid energy spectra show that there is a non-uniform distortion of the turbulence with a relative increase in small-scale energy. The non-uniform distortion significantly affects the transport of the dissipation rate, with the production and destruction of dissipation exhibiting completely different behaviors. The spectrum of the fluid-particle energy exchange rate shows that the fluid drags particles at low wavenumbers while the converse is true at high wavenumbers for small particles. A spectral analysis shows that the increase of the high wavenumber portion of the fluid energy spectrum can be attributed to transfer of the fluid-particle covariance by the fluid turbulence. This in turn explains the relative increase of small-scale energy caused by small particles observed in the present simulations as well as those of others.

Squires, Kyle D.↗

Ground-Based Lidar Measurements of Aerosols During ACE-2: Instrument Description, Results, and Comparisons with Other Ground-Based and Airborne Measurements

A micro-pulse lidar system (MPL) was used to measure the vertical and horizontal distribution of aerosols during the Aerosol Characterization Experiment 2 (ACE-2) in June and July of 1997. The MPL measurements were made at the Izana observatory (IZO), a weather station located on a mountain ridge (28 deg 18 min N, 16 deg 30 min W, 2367 m asl) near the center of the island of Tenerife, Canary Islands. The MPL was used to acquire aerosol backscatter, extinction, and optical depth profiles for normal background periods and periods influenced by Saharan dust from North Africa. System tests and calibration procedures are discussed, and an analysis of aerosol optical profiles acquired during ACE-2 is presented. MPL data taken during normal IZO conditions (no dust) showed that upslope aerosols appeared during the day and dissipated at night and that the layers were mostly confined to altitudes a few hundred meters above IZO. MPL data taken during a Saharan dust episode on 17 July showed that peak aerosol extinction values were an order of magnitude greater than molecular scattering over IZO, and that the dust layers extended to 5 km asl. The value of the dust backscatter-extinction ratio was determined to be 0.027 +/- 0.007 sr(exp -1). Comparisons of the MPL data with data from other collocated instruments showed good agreement during the dust episode.

Welton, Ellsworth J.↗

Consistency of ARESE II Cloud Absorption Estimates and Sampling Issues

Data from three cloudy days (March 3, 21, 29, 2000) of the ARM Enhanced Shortwave Experiment II (ARESE II) were analyzed. Grand averages of broadband absorptance among three sets of instruments were compared. Fractional solar absorptances were approx. 0.21-0.22 with the exception of March 3 when two sets of instruments gave values smaller by approx. 0.03-0.04. The robustness of these values was investigated by looking into possible sampling problems with the aid of 500 nm spectral fluxes. Grand averages of 500 nm apparent absorptance cover a wide range of values for these three days, namely from a large positive (approx. 0.011) average for March 3, to a small negative (approximately -0.03) for March 21, to near zero (approx. 0.01) for March 29. We present evidence suggesting that a large part of the discrepancies among the three days is due to the different nature of clouds and their non-uniform sampling. Hence, corrections to the grand average broadband absorptance values may be necessary. However, application of the known correction techniques may be precarious due to the sparsity of collocated flux measurements above and below the clouds. Our analysis leads to the conclusion that only March 29 fulfills all requirements for reliable estimates of cloud absorption, that is, the presence of thick, overcast, homogeneous clouds.

Oreopoulos, L.↗

Lidar Observations of Tropospheric Aerosols Over Northeastern South Africa During the ARREX and SAFARI-2000 Dry Season Experiments

During the ARREX-1999 and SAFARI-2000 Dry Season experiments a micropulse lidar (523 nm) instrument was operated at the Skukuza Airport in northeastern South Africa. The Mar was collocated with a diverse array of passive radiometric equipment. For SAFARI-2000 the processed Mar data yields a daytime time-series of layer mean/derived aerosol optical properties, including extinction-to-backscatter ratios and vertical extinction cross-section profile. Combined with 523 run aerosol optical depth and spectral Angstrom exponent calculations from available CIMEL sun-photometer data and normalized broadband flux measurements the temporal evolution of the near surface aerosol layer optical properties is analyzed for climatological trends. For the densest smoke/haze events the extinction-to-backscatter ratio is found to be between 60-80/sr, and corresponding Angstrom exponent calculations near and above 1.75. The optical characteristics of an evolving smoke event from SAFARI-2000 are extensively detailed. The advecting smoke was embedded within two distinct stratified thermodynamic layers, causing the particulate mass to advect over the instrument array in an incoherent manner on the afternoon of its occurrence. Surface broadband flux forcing due to the smoke is calculated, as is the evolution in the vertical aerosol extinction profile as measured by the Han Finally, observations of persistent elevated aerosol during ARREX-1999 are presented and discussed. The lack of corroborating observations the following year makes these observation; both unique and noteworthy in the scope of regional aerosol transport over southern Africa.

Campbell, James R.↗

A Localized Tau Method PDE Solver

In this paper we present a new form of the collocation method that allows one to find very accurate solutions to time marching problems without the unwelcome appearance of Gibb's phenomenon oscillations. The basic method is applicable to any partial differential equation whose solution is a continuous, albeit possibly rapidly varying function. Discontinuous functions are dealt with by replacing the function in a small neighborhood of the discontinuity with a spline that smoothly connects the function segments on either side of the discontinuity. This will be demonstrated when the solution to the inviscid Burgers equation is discussed.

Cottam, Russell↗