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At least 361 records · Page 20
All sourcesNASA NTRSDOE OSTI
DOE OSTI2017

The Effects of Magnetic Fields on the Dynamics of Radiation Pressure–dominated Massive Star Envelopes

We use three-dimensional radiation magnetohydrodynamic simulations to study the effects of magnetic fields on the energy transport and structure of radiation pressure–dominated main sequence massive star envelopes at the region of the iron opacity peak. We focus on the regime where the local thermal timescale is shorter than the dynamical timescale, corresponding to inefficient convective energy transport. We begin with initially weak magnetic fields relative to the thermal pressure, from 100 to 1000 G in differing geometries. The unstable density inversion amplifies the magnetic field, increasing the magnetic energy density to values close to equipartition with the turbulent kinetic energy density. By providing pressure support, the magnetic field's presence significantly increases the density fluctuations in the turbulent envelope, thereby enhancing the radiative energy transport by allowing photons to diffuse out through low-density regions. Magnetic buoyancy brings small-scale magnetic fields to the photosphere and increases the vertical energy transport, with the energy advection velocity proportional to the Alfvén velocity, although in all cases we study, photon diffusion still dominates the energy transport. The increased radiative and advective energy transport causes the stellar envelope to shrink by several scale heights. We also find larger turbulent velocity fluctuations compared with the purely hydrodynamic case, reaching $\approx 100\,{{\rm{km}}{\rm{s}}}^{-1}$ at the stellar photosphere. The photosphere also shows vertical oscillations with similar averaged velocities and periods of a few hours. The increased turbulent velocity and oscillations will have strong impacts on the line broadening and periodic signals in massive stars.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Islet: interpolation semi-Lagrangian element-based transport

Abstract. Advection of trace species, or tracers, also called tracer transport, in models of the atmosphere and other physical domains is an important and potentially computationally expensive part of a model's dynamical core. Semi-Lagrangian (SL) advection methods are efficient because they permit a time step much larger than the advective stability limit for explicit Eulerian methods without requiring the solution of a globally coupled system of equations as implicit Eulerian methods do. Thus, to reduce the computational expense of tracer transport, dynamical cores often use SL methods to advect tracers. The class of interpolation semi-Lagrangian (ISL) methods contains potentially extremely efficient SL methods. We describe a finite-element ISL transport method that we call the interpolation semi-Lagrangian element-based transport (Islet) method, such as for use with atmosphere models discretized using the spectral element method. The Islet method uses three grids that share an element grid: a dynamics grid supporting, for example, the Gauss–Legendre–Lobatto basis of degree three; a physics parameterizations grid with a configurable number of finite-volume subcells per element; and a tracer grid supporting use of Islet bases with particular basis again configurable. This method provides extremely accurate tracer transport and excellent diagnostic values in a number of verification problems.

58 GEOSCIENCES↗
DOE OSTI2018

Does elevated atmospheric CO 2 affect soil carbon burial and soil weathering in a forest ecosystem?

Most experimental studies measuring the effects of climate change on terrestrial C cycling have focused on processes that occur at relatively short time scales (up to a few years). However, climate-soil C interactions are influenced over much longer time scales by bioturbation and soil weathering affecting soil fertility, ecosystem productivity, and C storage. Elevated CO 2 can increase belowground C inputs and stimulate soil biota, potentially affecting bioturbation, and can decrease soil pH which could accelerate soil weathering rates. To determine whether we could resolve any changes in bioturbation or C storage, we investigated soil profiles collected from ambient and elevated-CO 2 plots at the Free-Air Carbon-Dioxide Enrichment (FACE) forest site at Oak Ridge National Laboratory after 11 years of 13 C-depleted CO 2 release. Profiles of organic carbon concentration, δ 13 C values, and activities of 137 Cs, 210 Pb, and 226 Ra were measured to ~30 cm depth in replicated soil cores to evaluate the effects of elevated CO 2 on these parameters. Bioturbation models based on fitting advection-diffusion equations to 137 Cs and 210 Pb profiles showed that ambient and elevated-CO 2 plots had indistinguishable ranges of apparent biodiffusion constants, advection rates, and soil mixing times, although apparent biodiffusion constants and advection rates were larger for 137 Cs than for 210 Pb as is generally observed in soils. Temporal changes in profiles of δ 13 C values of soil organic carbon (SOC) suggest that addition of new SOC at depth was occurring at a faster rate than that implied by the net advection term of the bioturbation model. Ratios of ( 210 Pb/ 226 Ra) may indicate apparent soil mixing cells that are consistent with biological mechanisms, possibly earthworms and root proliferation, driving C addition and the mixing of soil between ~4 cm and ~18 cm depth. Lastly, burial of SOC by soil mixing processes could substantially increase the net long-term storage of soil C and should be incorporated in soil-atmosphere interaction models.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS1973

A field investigation and numerical simulation of coastal fog

A field investigation of the microphysical and micrometeorological features of fogs occurring near Los Angeles and Vandenberg, California was conducted. Observations of wind speed and direction, temperature, dew point, vertical wind velocity, dew deposition, drop-size distribution, liquid water content, and haze and cloud nucleus concentration were obtained. These observations were initiated in late evening prior to fog formation and continued until the time of dissipation in both advection and radiation fogs. Data were also acquired in one valley fog and several dense haze situations. The behavior of these parameters prior to and during fog are discussed in detail. A two-dimensional numerical model was developed to investigate the formation and dissipation of advection fogs under the influence of horizontal variations in surface temperature. The model predicts the evolution of potential temperature, water vapor content, and liquid water content in a vertical plane as determined by vertical turbulent transfer and horizontal advection. Results are discussed from preliminary numerical experiments on the formation of warm-air advection fog and dissipation by natural and artificial heating from the surface.

Mack, E. J.↗
NASA NTRS1982

The effects of random errors in rawinsonde data on derived kinematic quantities

The sensitivity of kinematic parameters to random errors contained in rawinsonde data is assessed. Parameters under consideration include relative vorticity, vorticity advection, horizontal divergence, kinematic vertical motion, and temperature advection. It is shown that horizontal divergence is the most affected, with reliability a function of height. Vorticity advection is the next most altered by random error, and in this case, the effects of wind errors are greater on the gradient of vorticity than on the vorticity itself. Vertical motions are most affected by random perturbations at 300 mb and above, and temperature advection is found to be the least sensitive to random perturbations.

Belt, C. L.↗
NASA NTRS1991

Characteristics-based methods applied to infinite Prandtl number thermal convection in the hard turbulent regime

Characteristics-based methods for the advection-diffusion equation are presented and directly applied to study thermal convection with extremely large Rayleigh number (Ra). It is shown that the operator-splitting method for advection-diffusion problems is very accurate for determining the advected field at extremely high Peclet number (Pe). The technique presented is considered to have great potential for solving advection-dominated problems, while the Langrangian method is more accurate for lower Pe. It is noted that the accuracy of these characteristics-based methods strongly depends on the quality of interpolation. The computational time for the operator-splitting method grows with the number of time steps employed. The Langrangian method was used for simulations of convection at very high Ra, up to 3 x 10 to the 9th, and time-dependent, thermal convection solutions were obtained for infinite Prandtl number.

Malevsky, A. V.↗
NASA NTRS1993

The role of atmospheric heat transport in the seasonal carbon dioxide cycle

We have carried out numerical experiments with a general circulations model (GCM) and energy balance model of the martian atmosphere to define the importance of heat transported to the polar regions in determining the amount of CO2 condensed on the surface during the fall and winter seasons and the amount sublimated during the spring and summer seasons. In so doing, we performed both sensitivity experiments, in which the dust opacity was varied over the full range of its observed values, and annual simulations, in which the dust opacity varied continuously with seasonal data, in accord with measurements taken at the Viking landers. Dust opacity represents the key variable for determining the contribution of atmospheric heat advection to the energy budget in the polar regions. The amount of heat advected to the winter polar regions increases monotonically as the dust opacity at low and middle latitudes increases. However, the increase is sharpest between optical depths of 0 and 1 tends to level off at still higher optical depths. Heat advection is more important at times of CO2 condensation than CO2 sublimation, since the temperature gradients are much steeper in the winter hemisphere than in the summer hemisphere. Because dust opacity is much higher during northern winter than during southern winter, atmospheric heat advection reduces the amount of CO2 that condenses in the north by a much larger factor than it does in the south.

Pollack, James B.↗
NASA NTRS1994

Interannual variability in stratiform cloudiness and sea surface temperature

Marine stratiform cloudiness (MSC)(stratus, stratocumulus, and fog) is widespread over subtropical oceans west of the continents and over midlatitude oceans during summer, the season when MSC has maximum influence on surface downward radiation and is most influenced by boundary-layer processes. Long-term datasets of cloudiness and sea surface teperature (SST) from surface observations from 1952 to 1981 are used to examine interannual variations in MSC and SST. Linear correlations of anomalies in seasonal MSC amount with seasonal SST anomalies are negative and significant in midlatitude and eastern subtropical oceans, especially during summer. Significant negative correlations between SST and nimbostratus and nonprecipitating midlevel cloudiness are also observed at midlatitudes during summer, suggesting that summer storm tracks shift from year to year following year-to-year meridional shifts in the SST gradient. Over the 30-yr period, there are significant upward trends in MSC amount over the northern midlatitude oceans and a significant downward trend off the coast of California. The highest correlations and trends occur where gradients in MSC and SST are strongest. During summer, correlations between SST and MSC anomalies peak at zero lag in midlatitudes where warm advection prevails, but SST lags MSC in subtropical regions where cold advection predominates. This difference is attributed to a tendency for anomalies in latent heat flux to compensate anomalies in surface downward radiation in warm advection regions but not in cold advection regions.

Norris, Joel R.↗
NASA NTRS1995

Planetary and synoptic-scale interactions during the life cycle of a mid-latitude blocking anticyclone over the North Atlantic

The formation of a blocking anticyclone over the North Atlantic has been examined over its entire life-CyCle using the Zwack-Okossi (Z-O) equation as the diagnostic tool. This blocking anticyclone occurred in late October and early November of 1985. The data used were provided by the NASA Goddard Laboratory for Atmospheres on a global 2.O degree latitude by 2.5 degree longitudinal grid. The horizontal distribution of the atmospheric forcing mechanisms that were important to 500 mb block formation, maintenance and decay were examined. A scale-partitioned form of the Z-O equation was then used to examine the relative importance of forcing on the planetary and synoptic scales, and their interactions. As seen in previous studies, the results presented here show that upper tropospheric anticyclonic vorticity advection was the most important contributor to block formation and maintenance. However, adiabatic warming, and vorticity tilting were also important at various times during the block lifetime. In association with precursor surface cyclogenesis, the 300 mb jet streak in the downstream (upstream) from a long-wave trough (ridge) amplified significantly. This strengthening of the jet streak enhanced the anti-cyclonic vorticity advection field that aided the amplification of a 500 mb short-wave ridge. Tile partitioned height tendency results demonstrate that the interactions between the planetary and sn,noptic-scale through vorticity advection was the most important contributor to block formation. Planetary-scale, synoptic-scale. and their interactions contributed weakly to the maintenance of the blocking anticyclone with the advection of synoptic-scale vorticity by the planetary-scale flow playing a more important role. Planetary-scale decay ofthe long-wave ridge contributed to the demise of this blocking event.

Smith, Phillip J.↗
NASA NTRS1999

Mechanism for Surface Warming in the Equatorial Pacific during 1994-95

Mechanisms controlling the variation in sea surface temperature warm event in the equatorial Pacific were investigated through ocean model simulations. In addition, the mechanisms of the climatological SST cycle were investigated. The dominant mechanisms governing the seasonal cycle of SST vary significantly across the basin. In the western Pacific the annual cycle of SST is primarily in response to external heat flux. In the central basin the magnitude of zonal advection is comparable to that of the external heat flux. In the eastern basin the role of zonal advection is reduced and the vertical mixing is more important. In the easternmost equatorial Pacific the vertical entrainment contribution is as large as that of vertical diffusion. The model estimate of the vertical mixing contribution to the mixed layer heat budget compared well with estimates obtained by analysis of observations using the same diagnostic vertical mixing scheme. During 1994- 1995 the largest positive SST anomaly was observed in the mid-basin and was related to reduced latent heat flux due to weak surface winds. In the western basin the initial warming was related to enhanced external heating and reduced cooling effects of both vertical mixing and horizontal advection associated with weaker than usual wind stress. In the eastern Pacific where winds were not significantly anomalous throughout 1994-1995, only a moderate warm surface anomaly was detected. This is in contrast to strong El Nino events where the SST anomaly is largest in the eastern basin and, as shown by previous studies, the anomaly is due to zonal advection rather than anomalous surface heat flux. The end of the warm event was marked by cooling in July 1995 everywhere across the equatorial Pacific.

Rienecker, Michele M.↗
NASA NTRS2001

The DROPPS/MIDAS Campaign Neutral Atmosphere Measurements and the Occurrence of PMSE and NLC

Measurements of the neutral atmosphere and their relationship to electrodynamic conditions in the mesosphere have been of interest for many years. Inflatable falling sphere measurements along with electrodynamic measurements were obtained in conjunction with the occurrence of PMSE and NLC during the DROPPS/MIDAS Campaign conducted in July 1999 from Andenes Rocket Range, Norway. The inflatable failing sphere measurements in conjunction with a PMSE event on 5-6 July and with a NLC event on 14 July are used to infer thermal advection and its influence on the clouds' maintenance. Hodograph analysis, an early tropospheric tool used by analyst and forecasters, will be used to determine the magnitude and direction of thermal advection from measured wind data. Analysis of the wind structure through the use of hodographs and some assumptions can determine thermal advection, wind shear, and possible vertical motion. Changes in the temperature structure between allied observations were subtle which may be explained by advection. Because of meteorological instabilities in the mesosphere it is possible that hodograph analysis may not fully work. It is our intention to show that such analysis has value and has a place in the mesosphere.

Schmidlin, F. J.↗
NASA NTRS2001

Warm-Core Intensification Through Horizontal Eddy Heat Transports into the Eye

A simulation of Hurricane Bob (1991) using the PSU/NCAR MM5 mesoscale model with a finest mesh spacing of 1.3 km is used to diagnose the heat budget of the hurricane. Heat budget terms, including latent and radiative heating, boundary layer forcing, and advection terms were output directly from the model for a 6-h period with 2-min frequency. Previous studies of warm core formation have emphasized the warming associated with gentle subsidence within the eye. The simulation of Hurricane Bob confirms subsidence warming as a major factor for eye warming, but also shows a significant contribution from horizontal advective terms. When averaged over the area of the eye, subsidence is found to strongly warm the mid-troposphere (2-9 km) while horizontal advection warms the mid to upper troposphere (5-13 km) with about equal magnitude. Partitioning of the horizontal advective terms into azimuthal mean and eddy components shows that the mean radial circulation does not, as expected, generally contribute to this warming, but that it is produced almost entirely by the horizontal eddy transport of heat into the eye. A further breakdown of the eddy components into azimuthal wave numbers 1, 2, and higher indicates that the warming is dominated by wave number 1 asymmetries, with smaller coming from higher wave numbers. Warming by horizontal eddy transport is consistent with idealized modeling of vortex Rossby waves and work is in progress to identify and clarify the role of vortex Rossby waves in warm-core intensification in both the full-physics model and idealized models.

Braun, Scott A.↗
NASA NTRS2001

Interactions Between the Thermohaline Circulation and Tropical Atlantic SST in a Coupled General Circulation Model

Tropical Atlantic SST shows a (statistically well-defined) decadal time scale in a 104-year simulation of unforced variability by a coupled general circulation model (CGCM). The SST anomalies superficially resemble observed Tropical Atlantic variability (TAV), and are associated with changes in the atmospheric circulation. Brazilian rainfall is modulated with a decadal time scale, along with the strength of the Atlantic trade winds, which are associated with variations in evaporation and the net surface heat flux. However, in contrast to observed tropical Atlantic variability, the trade winds damp the associated anomalies in ocean temperature, indicating a negative feedback. Tropical SST anomalies in the CGCM, though opposed by the surface heat flux, are advected in from the Southern Hemisphere mid-latitudes. These variations modulate the strength of the thermohaline circulation (THC): warm, salty anomalies at the equator sink drawing cold, fresh mid-latitude water. Upon reaching the equator, the latter inhibit vertical overturning and advection from higher latitudes, which allows warm, salty anomalies to reform, returning the cycle to its original state. Thus, the cycle results from advection of density anomalies and the effect of these anomalies upon the rate of vertical overturning and surface advection. This decadal modulation of Tropical Atlantic SST and the thermohaline circulation is correlated with ocean heat transport to the Northern Hemisphere high latitudes and Norwegian Sea SST. Because of the central role of equatorial convection, we question whether this mechanism is present in the current climate, although we speculate that it may have operated in palaeo times, depending upon the stability of the tropical water column.

Miller, Ron↗
NASA NTRS2001

Warm-Core Intensification of a Hurricane Through Horizontal Eddy Heat Transports Inside the Eye

A simulation of Hurricane Bob (1991) using the PSU/NCAR MM5 mesoscale model with a finest mesh spacing of 1.3 km is used to diagnose the heat budget of the hurricane. Heat budget terms, including latent and radiative heating, boundary layer forcing, and advection terms were output directly from the model for a 6-h period with 2-min frequency. Previous studies of warm core formation have emphasized the warming associated with gentle subsidence within the eye. The simulation of Hurricane Bob also identifies subsidence warming as a major factor for eye warming, but also shows a significant contribution from horizontal advective terms. When averaged over the area of the eye, excluding the eyewall (at least in an azimuthal mean sense), subsidence is found to strongly warm the mid-troposphere (2-9 km) while horizontal advection warms the mid to upper troposphere (5-13 km) with about equal magnitude. Partitioning of the horizontal advective terms into azimuthal mean and eddy components shows that the mean radial circulation cannot, as expected, generally contribute to this warming, but that it is produced almost entirely by the horizontal eddy transport of heat into the eye. A further breakdown of the eddy components into azimuthal wave numbers 1, 2, and higher indicates that the warming is dominated by wave number 1 asymmetries, with smaller contributions coming from higher wave numbers. Warming by horizontal eddy transport is consistent with idealized modeling of vortex Rossby waves and work is in progress to identify and clarify the role of vortex Rossby waves in warm-core intensification in both the full-physics model and idealized models.

Braun, Scott A.↗
NASA NTRS2002

Variability of Winter Air Temperature in Mid-Latitude Europe

The aim of this paper is to report extreme winter/early-spring air temperature (hereinafter temperature) anomalies in mid-latitude Europe, and to discuss the underlying forcing to these interannual fluctuations. Warm advection from the North Atlantic in late winter controls the surface-air temperature, as indicated by the substantial correlation between the speed of the surface southwesterlies over the eastern North Atlantic (quantified by a specific Index Ina) and the 2-meter level air temperatures (hereinafter Ts) over Europe, 45-60 deg N, in winter. In mid-March and subsequently, the correlation drops drastically (quite often it is negative). This change in the relationship between Ts and Ina marks a transition in the control of the surface-air temperature: absorption of insolation replaces the warm advection as the dominant control. This forcing by maritime-air advection in winter was demonstrated in a previous publication, and is re-examined here in conjunction with extreme fluctuations of temperatures in Europe. We analyze here the interannual variability at its extreme by comparing warm-winter/early-spring of 1989/90 with the opposite scenario in 1995/96. For these two December-to-March periods the differences in the monthly mean temperature in Warsaw and Torun, Poland, range above 10 C. Short-term (shorter than a month) fluctuations of the temperature are likewise very strong. We conduct pentad-by-pentad analysis of the surface-maximum air temperature (hereinafter Tmax), in a selected location, examining the dependence on Ina. The increased cloudiness and higher amounts of total precipitable water, corollary effects to the warm low-level advection. in the 1989/90 winter, enhance the positive temperature anomalies. The analysis of the ocean surface winds is based on the Special Sensor Microwave/Imager (SSM/I) dataset; ascent rates, and over land wind data are from the European Centre for Medium-Range Weather Forecasts (ECMWF); maps of 2-m temperature, cloud cover and precipitable water are from the National Centers for Environmental Prediction (NCEP) Reanalysis.

Otterman, J.↗
NASA NTRS2003

Cloud Modeling Using Field Project Data for the Study of Precipitation Processes

The use of cloud-resolving models (CRMs) in the study of precipitation process and their relation to the large-scale environment can be generally categorized into two approaches. The first approach is so called "cloud ensemble modeling". In this approach, many clouds of different size in various stages of their lifecycles can be present at any model simulation time. Large-scale effects are derived from observations and imposed into the model as the main forcing. The advantage of this approach is that the modeled convection will be forced to have the same intensity, thermodynamic budget and organization as the obserations.This approach will also allow CRMs to perform multi-day or multi-week time integrations. The second approach usually requires initial temperature and water vapor profiles that have a medium to large CAPE, and open lateral boundary conditions are used. The modeled clouds could be termed "self-forced convection". Model improvements, such as in the microphysics, are achieved using the second approach. In cloud ensemble modeling, accurate large-scale advective tendencies for temperature and water vapor are the main forcing for the CRMs. We found that the large-scale advective terms for temperature and water vapor are not always consistent, For example, large-scale forcing could indicate strong drying which would produce cooling in the model through evaporation but not contain large-scale advective heating to compensate. This discrepancy in forcing would cause differences between the observed and modeled latent heating profiles. Good measurements of other quantities (i.e., surface fluxes and radiation) are also required to perform variational objective analysis that computes and minimizes a "cost function" that constrains the difference between the large-scale advective forcing in temperature and water vapor. With self-forced convection, accurate vertical distributions of temperature, moisture (water vapor), and horizontal winds are required. The timing of the measurements relative to cloud development is crucial (i.e., prior to cloud triggering). Microphysical measurements (i.e., the cloud number concentration and size distribution) can also be used in this second approach but are of secondary importance with cloud ensemble modeling. In this paper, data collected during TRMM field campaigns (FCs; i.e., SCSMEX, LBA and KWAJEX) which were aimed at validating TRMM products (i.e., rainfall and the vertical distribution of latent heating) will be used to examine the impact of errors in the initial conditions (e.g.., soundings an large-scale forcing) on simulated rainfall distributions and brightness. Rainfall and precipitations simulated from a CRM will also be compared with those estimated by a schocastic model.

Tao, W.-K.↗
NASA NTRS2003

Transport Equation Based Wall Distance Computations Aimed at Flows With Time-Dependent Geometry

Eikonal, Hamilton-Jacobi and Poisson equations can be used for economical nearest wall distance computation and modification. Economical computations may be especially useful for aeroelastic and adaptive grid problems for which the grid deforms, and the nearest wall distance needs to be repeatedly computed. Modifications are directed at remedying turbulence model defects. For complex grid structures, implementation of the Eikonal and Hamilton-Jacobi approaches is not straightforward. This prohibits their use in industrial CFD solvers. However, both the Eikonal and Hamilton-Jacobi equations can be written in advection and advection-diffusion forms, respectively. These, like the Poisson s Laplacian, are commonly occurring industrial CFD solver elements. Use of the NASA CFL3D code to solve the Eikonal and Hamilton-Jacobi equations in advective-based forms is explored. The advection-based distance equations are found to have robust convergence. Geometries studied include single and two element airfoils, wing body and double delta configurations along with a complex electronics system. It is shown that for Eikonal accuracy, upwind metric differences are required. The Poisson approach is found effective and, since it does not require offset metric evaluations, easiest to implement. The sensitivity of flow solutions to wall distance assumptions is explored. Generally, results are not greatly affected by wall distance traits.

Tucker, Paul G.↗
NASA NTRS2003

Transport Equation Based Wall Distance Computations Aimed at Flows With Time-Dependent Geometry

Eikonal, Hamilton-Jacobi and Poisson equations can be used for economical nearest wall distance computation and modification. Economical computations may be especially useful for aeroelastic and adaptive grid problems for which the grid deforms, and the nearest wall distance needs to be repeatedly computed. Modifications are directed at remedying turbulence model defects. For complex grid structures, implementation of the Eikonal and Hamilton-Jacobi approaches is not straightforward. This prohibits their use in industrial CFD solvers. However, both the Eikonal and Hamilton-Jacobi equations can be written in advection and advection-diffusion forms, respectively. These, like the Poisson's Laplacian, are commonly occurring industrial CFD solver elements. Use of the NASA CFL3D code to solve the Eikonal and Hamilton-Jacobi equations in advective-based forms is explored. The advection-based distance equations are found to have robust convergence. Geometries studied include single and two element airfoils, wing body and double delta configurations along with a complex electronics system. It is shown that for Eikonal accuracy, upwind metric differences are required. The Poisson approach is found effective and, since it does not require offset metric evaluations, easiest to implement. The sensitivity of flow solutions to wall distance assumptions is explored. Generally, results are not greatly affected by wall distance traits.

Tucker, Paul G.↗