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DOE OSTI2023

Temperature uncertainty modelling with proxy structural data as geostatistical constraints for well siting: an example applied to Granite Springs Valley, NV, USA

Utilizing existing temperature and structural geology information around Granite Springs Valley, Nevada, we build 3D stochastic temperature models with the aims of evaluating the 3D uncertainty of temperature and choosing between candidate exploration well locations. The data used to support the modelling are measured temperatures and structural proxies from 3D geologic modelling (distance to fault, distance to fault intersections and terminations, Coulomb stress change and dilation tendency), the latter considered ‘secondary’ data. Two stochastic geostatistical techniques are explored for incorporating the structural proxies: cosimulation and local varying mean. With both the cosimulation and local varying mean methods, many equally-likely temperature models (i.e. realizations) are produced, from which temperature probability profiles are calculated at candidate well locations. To aid in choosing between the candidate locations, two quantities summarize the temperature probabilities: V prior and entropy. V prior quantifies the likelihood for economic temperatures at each candidate location, whereas entropy identifies where new information has the most potential to reduce uncertainty. In general, the cosimulation realizations have smoother spatial structure, and extrapolate high temperatures at candidate locations that are located along the direction of the longest spatial correlation, which are down dip from existing temperature logs. The smooth realizations result in tight temperature probability profiles that are easier to interpret, but they have unrealistic temperature reversals in some locations because of the dipping ellipsoid shape created and that the cosimulation technique does not enforce a conductive geothermal gradient as a baseline (i.e. linearly increasing temperature with depth). The local varying mean results produce realizations with more realistic geothermal gradients, with temperatures increasing downward since a depth-temperature relationship is included. However, because they have much noisier spatial nature compared to cosimulation, it is harder to interpret the temperature probability profiles. The different local varying mean results allow the geologist to determine which proxy (e.g. dilation v. distance to fault termination) should be used given the specific geothermal system. In general, V prior from local varying mean results identify locations that are close to high values for the structural proxies: areas with higher probabilities for higher temperatures. The entropy results identify where uncertainty is greatest and therefore new drilling information could be most useful. Though these techniques provide useful information, even when applied to areas of sparse data, our comparison of these two techniques demonstrates the need for new geothermal geostatistics techniques that combine the advantages of these two methods and that are tailored to the spatial uncertainty issues inherent in geothermal exploration.

15 GEOTHERMAL ENERGY↗

DOE OSTI2020

2020 Annual Report of Available Drawdowns for Each Oil Storage Cavern in the Strategic Petroleum Reserve

The Department of Energy maintains an up-to-date documentation of the number of available full drawdowns of each of the caverns owned by the Strategic Petroleum Reserve (SPR). This information is important for assessing the SPR's ability to deliver oil to domestic oil companies expeditiously if national or world events dictate a rapid sale and deployment of the oil reserves. Sandia was directed to develop and implement a process to continuously assess and report the evolution of drawdown capacity, the subject of this report. A cavern has an available drawdown if after that drawdown, the long-term stability of the cavern, the cavern field, or the oil quality are not compromised. Thus, determining the number of available drawdowns requires the consideration of several factors regarding cavern and wellbore integrity and stability, including stress states caused by cavern geometry and operations, salt damage caused by dilatant and tensile stresses, the effect of enhanced creep on wellbore integrity, and the sympathetic stress effect of operations on neighboring caverns. A consensus has now been built regarding the assessment of drawdown capabilities and risks for the SPR caverns. The process involves an initial assessment of the pillar-to-diameter (P/D) ratio for each cavern with respect to neighboring caverns. A large pillar thickness between adjacent caverns should be strong enough to withstand the stresses induced by closure of the caverns due to salt creep. The first evaluation of P/D includes a calculation of the evolution of P/D after a number of full cavern drawdowns. The most common storage industry standard is to keep this value greater than 1.0, which should ensure a pillar thick enough to prevent loss of fluids to the surrounding rock mass. However, many of the SPR caverns currently have a P/D less than 1.0 or will likely have a low P/D after one or two full drawdowns. For these caverns, it is important to examine the structural integrity with more detail using geomechanical models. Finite-element geomechanical models have been used to determine the stress states in the pillars following successive drawdowns. By computing the tensile and dilatant stresses in the salt, areas of potential structural instability can be identified that may represent "red flags" for additional drawdowns. These analyses have found that many caverns will maintain structural integrity even when grown via drawdowns to dimensions resulting in a P/D of less than 1.0. The analyses have also confirmed that certain caverns should only be completely drawn down one time. As the SPR caverns are utilized and partial drawdowns are performed to remove oil from the caverns (e.g., for occasional oil sales authorized by the Congress or the President), the changes to the cavern caused by these procedures must be tracked and accounted for so that an ongoing assessment of the cavern's drawdown capacity may be continued. A proposed methodology for assessing and tracking the available drawdowns for each cavern was presented in Sobolik et al. (2018). This report includes an update to the baseline drawdowns for each cavern, and provides an initial assessment of the evolution of drawdown expenditure for several caverns

02 PETROLEUM↗

DOE OSTI2021

Available Drawdowns for Each Oil Storage Cavern in the Strategic Petroleum Reserve (2021 Annual Report)

The Department of Energy maintains an up-to-date documentation of the number of available full drawdowns of each of the caverns owned by the Strategic Petroleum Reserve (SPR). This information is important for assessing the SPRs ability to deliver oil to domestic oil companies expeditiously if national or world events dictate a rapid sale and deployment of the oil reserves. Sandia was directed to develop and implement a process to continuously assess and report the evolution of drawdown capacity, the subject of this report. A cavern has an available drawdown if after that drawdown, the long-term stability of the cavern, the cavern field, or the oil quality are not compromised. Thus, determining the number of available drawdowns requires the consideration of several factors regarding cavern and wellbore integrity and stability, including stress states caused by cavern geometry and operations, salt damage caused by dilatant and tensile stresses, the effect of enhanced creep on wellbore integrity, and the sympathetic stress effect of operations on neighboring caverns. A consensus has now been built regarding the assessment of drawdown capabilities and risks for the SPR caverns (Sobolik et al., 2014; Sobolik 2016). The process involves an initial assessment of the pillar - to - diameter (P/D) ratio for each cavern with respect to neighboring caverns. A large pillar thickness between adjacent caverns should be strong enough to withstand the stresses induced by closure of the caverns due to salt creep. The first evaluation of P/D includes a calculation of the evolution of P/D after a number of full cavern drawdowns. The most common storage industry standard is to keep this value greater than 1.0, which should ensure a pillar thick enough to prevent loss of fluids to the surrounding rock mass. However, many of the SPR caverns currently have a P/D less than 1.0 or will likely have a low P/D after one or two full drawdowns. For these caverns, it is important to examine the structural integrity with more detail using geomechanical models. Finite-element geomechanical models have been used to determine the stress states in the pillars following successive drawdowns. By computing the tensile and dilatant stresses in the salt, areas of potential structural instability can be identified that may represent red flags for additional drawdowns. These analyses have found that many caverns will maintain structural integrity even when grown via drawdowns to dimensions resulting in a P/D of less than 1.0. The analyses have also confirmed that certain caverns should only be completely drawn down one time. As the SPR caverns are utilized and partial drawdowns are performed to remove oil from the caverns (e.g., for occasional oil sales , purchases, or exchanges authorized by the Congress or the President), the changes to the cavern caused by these procedures must be tracked and accounted for so that an ongoing assessment of the caverns drawdown capacity may be continued. A proposed methodology for assessing and tracking the available drawdowns for each cavern was presented in Sobolik et al. (2018). This report is the latest in a series of annual reports, and it includes the baseline available drawdowns for each cavern, and the most recent assessment of the evolution of drawdown expenditure for several caverns .

02 PETROLEUM↗

DOE OSTI2022

Available Drawdowns for Each Oil Storage Cavern in the Strategic Petroleum Reserve (2022 Annual Report)

The Department of Energy maintains an up-to-date documentation of the number of available full drawdowns of each of the caverns owned by the Strategic Petroleum Reserve (SPR). This information is important for assessing the SPR's ability to deliver oil to domestic oil companies expeditiously if national or world events dictate a rapid sale and deployment of the oil reserves. Sandia was directed to develop and implement a process to continuously assess and report the evolution of drawdown capacity, the subject of this report. A cavern has an available drawdown if after that drawdown, the long-term stability of the cavern, the cavern field, or the oil quality are not compromised. Thus, determining the number of a vailable drawdowns requires the consideration of several factors regarding cavern and wellbore integrity and stability, including stress states caused by cavern geometry and operations, salt damage caused by dilatant and tensile stresses, the effect of enhanced creep on wellbore integrity, and the sympathetic stress effect of operations on neighboring caverns. A consensus has now been built regarding the assessment of drawdown capabilities and risks for the SPR caverns (Sobolik et al., 2014; Sobolik 2016). The process involves an initial assessment of the pillar-to-diameter (P/D) ratio for each cavern with respect to neighboring caverns. A large pillar thickness between adjacent caverns should be strong enough to withstand the stresses induced by closure of the caverns due to salt creep. The first evaluation of P/D includes a calculation of the evolution of P/D after a number of full cavern drawdowns. The most common storage industry standard is to keep this value greater than 1.0, which should ensure a pillar thick enough to prevent loss of fluids to the surrounding rock mass. However, many of the SPR caverns currently have a P/D less than 1.0 or will likely have a low P/D after one or two full drawdowns. For these caverns, it is important to examine the s tructural integrity with more detail using geomechanical models. Finite - element geomechanical models have been used to determine the stress states in the pillars following successive drawdowns. By computing the tensile and dilatant stresses in the salt, areas of potential structural instability can be identified that may represent "red flags" for additional drawdowns. These analyses have found that many caverns will maintain structural integrity even when grown via drawdowns to dimensions resulting in a P/D of less than 1.0. The analyses have also confirmed that certain caverns should only be completely drawn down one time. As the SPR caverns are utilized and partial drawdowns are performed to remove oil from the caverns (e.g., for occasional oil sales , purchases, or exchanges authorized by the Congress or the President), the changes to the cavern caused by these procedures must be tracked and accounted for so that an ongoing assessment of the cavern's drawdown capacity may be continued. A proposed methodology for assessing and tracking the available drawdowns for each cavern was presented in Sobolik et al. (2018). This report is the latest in a series of annual reports, and it includes the baseline available drawdowns for each cavern, and the most recent assessment of the evolution of drawdown expenditure for several caverns.

02 PETROLEUM↗

DOE OSTI2021

Geodyn Material Library: Pseudocap models for dry porous tocks

This report describes the second edition of the Pseudocap Strength models for porous rocks implemented in GEODYN material library. The first model was developed in 2007 and calibrated for concrete. Then, the model parameters were calibrated based on triaxial tests reported for limestones and sandstones of various porosities. In these models some key parameters were chosen as functions of the reference porosity,Φ. Since then multiple modifications were implemented in the model, therefore, it has been recalibrated for some common porous materials such as limestones, sandstones, alluvium, tuffs and granite. Two types of models are described in this repot. The first type (called Pseudocap Model or PM) is for rocks from a specific location. Parameters were calibrated for several specific geologic materials. The second type (called Generic Pseudocap Model or GPM) is useful for the sites where only basic information (rock type, porosity) is available. Generic models include built-in correlations between porosities and other mechanical properties observed for certain rock types. The models of both types were validated by comparing not only to quasi-static triaxial tests for these materials but also to shock Hugoniot data and spherical explosion data for some materials. All models were derived in the frame of isotropic plasticity. They are designed to be used in explicit finite element/difference codes. Tangent stiffness tensor is not provided but can be calculated numerically for the model to be used in implicit finite element codes. For an isotropic material the stress can be decomposed into volumetric and deviatoric parts. The volumetric part is modeled using an Equation of state (EOS) which calculates the pressure and the bulk sound speed as functions of the internal specific energy and density. Here a simple, Mie-Gruneisen EOS is presented, but tabulated EOS (LEOS) provided by the library can be used as well. The stress is limited by the yield surface which depends on three invariants of the stress tensor and specific internal energy. In addition, to capture the strain-rate dependence a simple multiplier is used for the yield surface which depends on the equivalent plastic strain rate. The failure surface (the ultimate yield, Y f , defined later) is chosen in the Hoek-Brown form, commonly used in rock mechanics. It includes measurable parameters such as Unconfined Compressive Strength (UCS) as well as scale parameters characterizing the quality of the rock such as GSI (Geologic Strength Index). Thus, even though the model is calibrated for small samples it offers a way to extrapolate the strength to the field scale using geological characterization of the rock mass. The model captures effects of brittle-ductile transition in rocks by introducing a cap multiplier to the yield function. The rate of dilatancy (bulking) is proportional to the slope of the yield surface affected by the cap. Therefore, it takes place only at low confinements when the pressure is less than the brittle-ductile transition pressure, P BD . On the contrary, the porous compaction takes place at pressures higher than P BD . The cap moves as the porosity is compacted or new porosity is generated due to dilatancy. The porous compaction is modeled using an evolution equation which includes deviatoric stress so that the onset of compaction corresponds to the cap surface. The model captures effects of shear-enhanced compaction which is an important for porous rocks. Section 2 describes the modeling framework and Section 3 presents the model calibration procedure. Section 4 compares experimental data for various rocks versus model predictions. The model parameters used for this comparison are given in Appendix. The files with material constants are available with the latest GEODYN material library distribution.

58 GEOSCIENCES↗

DOE OSTI2022

Ultrafast perturbation of magnetic domains by optical pumping in a ferromagnetic multilayer

Ultrafast optical pumping of systems with spatially nonuniform magnetic textures is known to cause far-from-equilibrium spin transport effects, such as the broadening of domain-walls. Here, we study the dynamics of labyrinth domain networks in ferromagnetic CoFe/Ni multilayers subject to a femtosecond optical pump and find an ultrafast domain dilation by 6% within 1.6 ps. This surprising result is based on the unambiguous determination of a harmonically-related shift of ultrafast magnetic X-ray diffraction for the first- and third-order rings. Domain dilation is plausible from conservation of momentum arguments, whereby inelastic scattering from a hot, quasi-ballistic, radial current transfers momentum to the magnetic domains. Our results suggest a potentially rich variety of unexpected physical phenomena associated with far-from-equilibrium inelastic electron-magnon scattering processes in the presence of spin textures.

36 MATERIALS SCIENCE↗

DOE OSTI2023

2023 Annual Report of Available Drawdowns for Each Oil Storage Cavern in the Strategic Petroleum Reserve

DOE maintains an up-to-date documentation of the number of available full drawdowns of each of the caverns at the U.S. Strategic Petroleum Reserve (SPR). This information is important for assessing the SPR’s ability to deliver oil to domestic oil companies expeditiously if national or world events dictate a rapid sale and deployment of the oil reserves. Sandia was directed to develop and implement a process to continuously assess and report the evolution of drawdown capacity, the subject of this report. This report covers impacts on drawdown availability due to SPR operations during Calendar Year 2022. A cavern has an available drawdown if, after that drawdown, the long-term stability of the cavern, the cavern field, or the oil quality are not compromised. Thus, determining the number of available drawdowns requires the consideration of several factors regarding cavern and wellbore integrity and stability, including stress states caused by cavern geometry and operations, salt damage caused by dilatant and tensile stresses, the effect of enhanced creep on wellbore integrity, and the sympathetic stress effect of operations on neighboring caverns. Finite-element geomechanical models have been used to determine the stress states in the pillars following successive drawdowns. By computing the tensile and dilatant stresses in the salt, areas of potential structural instability can be identified that may represent red flags for additional drawdowns. These analyses have found that many caverns will maintain structural integrity even when grown via drawdowns to dimensions resulting in a pillar-to-diameter ratio of less than 1.0. The analyses have also confirmed that certain caverns should only be completely drawn down one time. As the SPR caverns are utilized and partial drawdowns are performed to remove oil from the caverns (e.g., for oil sales, purchases, or exchanges authorized by the Congress or the President), the changes to the cavern caused by these procedures must be tracked and accounted for so that an ongoing assessment of the cavern’s drawdown capacity may be continued. A methodology for assessing and tracking the available drawdowns for each cavern is reiterated. This report is the latest in a series of annual reports, and it includes the baseline available drawdowns for each cavern, and the most recent assessment of the evolution of drawdown expenditures. A total of 222 million barrels of oil were released in calendar-year 2022. A nearly-equal amount of raw water was injected, resulting in an estimated 34 million barrels of cavern leaching. Twenty caverns have now expended a full drawdown. Cavern BC 18 has expended all its baseline available drawdowns, and has no drawdowns remaining. Cavern BM 103 has expended one of its two baseline drawdowns, and is now a single-drawdown cavern. All other caverns with an expenditure went from at-least-5 to at-least-4 remaining drawdowns.

02 PETROLEUM↗

DOE OSTI2026

Complete time-resolved X-ray shape capability for a 10 MJ implosion: Milestone Report for MRT 8818

This report documents completion of MRT 8818, which established an upgraded equatorial time-resolved X-ray imaging capability for high-yield inertial confinement fusion experiments at the National Ignition Facility (NIF) using the equatorial Dilation X-ray Imager (DIXI). The need for this work arose from the sustained increase in fusion yield at NIF, which progressively intensified the neutron and gamma-ray environment experienced by target diagnostics. Although the existing polar imaging capability, particularly the Polar Dilation X-ray Imager (PDIXI), remained viable at high yields, the equatorial capability became inadequate because of radiation-induced failure of electronic readout hardware and increasing background levels that degraded image quality and ultimately caused saturation. The work performed under MRT 8818 addressed this limitation through a combination of hardware replacement, background characterization, and targeted mitigation. The DIXI backend was converted from CCD-based electronic readout to photographic film, and the principal sources of internally generated background were investigated using prior analyses, dedicated tests, and comparison with PDIXI performance on high-yield shots. This effort led to implementation of two principal improvements: a multilayer optical coating to suppress broadband radiation-induced background generated in the fiber-optic extension cylinder, and replacement of Kodak TMAX 400 film with Agfa Copex Rapid to reduce background generated directly in the film. These upgrades were completed in 2025 and performance assessment based on DT shot data since then, comparing with Polar DIXI and scaling of these experiments to 10 MJ indicates an expected signal-to-background ratio of approximately 34 for a single pinhole image, substantially exceeding the MRT 8818 completion criterion of SNR > 5.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2022

Induced microearthquakes predict permeability creation in the brittle crust

Predicting the evolution of permeability accurately during stimulation at the reservoir scale and at the resolution of individual fractures is essential to characterize the fluid transport and the reactive/heat-transfer characteristics of reservoirs where stress exerts significant control. Here, we develop a hybrid machine learning (ML) model to visualize in situ permeability evolution for an intermediate-scale (~10 m) hydraulic stimulation experiment. This model includes an ML model that was trained using the well history of flow rate and wellhead pressure and MEQ data from the first three stimulation episodes to predict average permeability from the statistical features of the MEQs alone for later episodes. Moreover, a physics-inspired model is integrated to estimate in situ fracture permeability spatially. This method relates fracture permeability to fracture dilation and scales dilation to the equivalent MEQ magnitude, according to laboratory observations. The seismic data are then applied to define incremental changes in permeability in both space and time. Our results confirm the excellent agreement between the ground truth and model-predicted permeability evolution. The resulting permeability map defines and quantifies flow paths in the reservoir with the averaged permeability comparing favorably with the ground truth of permeability.

induced seismicity↗

NASA NTRS1971

Shock transmission in coupled beams and rib stiffened structures

Shock transmission in a simple coupled beam structure and in a ring-stringer stiffened cylinder is investigated experimentally and analytically using wave transmission and statistical energy analysis concepts. The use of the response spectrum to characterize the excitation provided to a simple beam by a force pulse is studied. Analysis of the transmission of a dilatation wave in a periodically stiffened plate indicates that the stiffeners are fairly transparent to the wave, but some of the dilatational energy is scattered into bending at each support.

Pope, L. D.↗

NASA NTRS1974

An improved method for echographic detection of left atrial enlargement

Echographic dimensions of the aortic root and left atrium were compared in 170 patients in order to assess dilation of the left atrium with reference to the relatively nondistensible fibrous aortic root. In 50 patients without cause for left atrial or aortic enlargement, the ratio of left atrial/aortic root dimensions was 0.87 to 1.11. In 80 patients with known cause for left atrial enlargement, the left atrial/aortic root ratio was greater than or equal to 1.17. In 40 patients with isolated valve disease, dilation of both the aortic root and the left atrium resulted in a left atrial/aortic root dimension ratio less than 1.17 in some patients. Despite this consideration, the comparison of left atrial and aortic root dimension appears to be as specific as, and more sensitive than, previously proposed methods for the evaluation of left atrial enlargement.

Brown, O. R.↗

NASA NTRS1975

Supersonic free turbulent mixing layers

A mean turbulent closure method with a length scale function is developed for predicting the reduced spreading rate in high Mach number, high Reynolds number free shear layers. The new feature of the method is the inclusion of effects of the pressure-dilation term which appears in the compressible form of the turbulence energy equation. The model indicates that the pressure-dilation correlation may act as a turbulence energy sink or source depending on whether the transverse gradients of mean Mach number and mean density have the same or opposite signs.

Oh, Y. H.↗

NASA NTRS1977

Noise transmission by viscoelastic sandwich panels

An analytical study on low frequency noise transmission into rectangular enclosures by viscoelastic sandwich panels is presented. Soft compressible cores with dilatational modes and hard incompressible cores with dilatational modes neglected are considered as limiting cases of core stiffness. It is reported that these panels can effect significant noise reduction.

Vaicaitis, R.↗

NASA NTRS1978

Linear and nonlinear interactions between the earth tide and a tectonically stressed earth

In the vincinity of earthquake focal regions, conditions may not be equal. Crustal rocks stressed to more than approximately 0.6 of their failure strength exhibit material properties over and above that of linear elasticity. Interactions between the earth tide and crustal rocks that are under high tectonic stress are discussed in terms of simple phenomenological models. In particular, the difference between a nonlinear elastic model of dilatancy and a dilatancy model that exhibits hysteresis is noted. It is concluded that the small changes in stress produced by the earth tide act as a probe of the properties of crustal rocks. Observations of earth tide tilts and strains in such high stress zones may, therefore, provide keys to the constitutive properties and the tectonic stress rate tensor of these zones.

Beaumont, C.↗

NASA NTRS1979

Effect of gravitation stress and hypokinesia on blood vessels of the testicle

Rabbits were exposed to single maximum endurable stresses of cranio-caudal direction, hypokinesia for periods of one to eight weeks, and hypokinesia followed by gravitation stresses. The stresses caused dilatation of vessels, greater sinuosity, and occasional ruptures of the walls and extravasation. The greater part of the capillaries were dilated; the greatest part constricted. In hypokinesia there was an increasing atrophy of the testes. Significant results are reported.

Palazhchenko, E. F.↗

NASA NTRS1980

Effect of gravitational overloads, hypokinesia and hypodynamia on the vessels of the pulmonary blood circuit

Vessels of the pulmonary circuit are studied under normal conditions, in exposure to single stress or continuous threshold endurable chestspine gravitational stresses, and one to eight weak hypokinesia and hypodynamic effects followed by stress. Examination methods include rentgenography and microrentgenography, clearing, and histology. In exposure to gravitational stress the distal portions of the arterial vessels of the 3 and 4 orders constrict, while all veins dilate. Sinuosity of all vessels is noted. The volume of the capillary bed increases and signs of perivascular edema occur. Due to hypokinesia and hypodynamia the arteries constricted and the arterial bed becomes poor. The veins of all orders dilate and the volume of the capillary bed increases. The changes grew greater the longer the terms of hypodyamic effects. Successive combination of hypokinesia and hypodynamia and gravitational stresses cause more pronounced changes than separate effects of these two factors and result in great deformity of the vascular walls, including their rupture and penetration of formed elements beyond the limits of the vascular bed.

Kasimtsev, A. A.↗

NASA NTRS1980

Effects of gravitational stress, hypokinesia and hypodynamia on the structure of the vascular bed of the spleen

The effects of two extreme factors, hypokinesia and hypodynamia, on spleen vascular beds were studied on 180 male and female albino rats. Vessels were studied by roentgenography, microroentgenography, clearing of sections and histology. Gravity stress yielded construction of all links of arterial bed and of order 5-7 veins. Large intraorganic vein diameters changed significantly but erratically. Hypokinesia in early phases produced pronounced spleen size reduction. Veins and arteries constricted along entire length. Later hypokinetic stages showed arteries still constricted; veins began to dilate from week 4 of hypokinesia. Sinuosity, uneven contours and varicose dilations of walls in large arteries and veins occurred. Abrupt changes in parenchyma, e.g., atrophy of folliculi, narrowing of lumen of central arteries from thickening of muscular wall. After exposure to hypokinesia followed by gravitational stress, pronounced lesions such as deformation of vascular wall, including rupture, in all vessels of the spleen vascular bed.

Nesterenko, N. T.↗

NASA NTRS1982

Solutions of the compressible Navier-Stokes equations using the integral method

The integral representation method was used to obtain numerical solutions of the compressible, unsteady, two-dimensional Navier-Stokes equations for subsonic flows. The equations were written with the vorticity, the dilatation, the density, and the enthalpy as the dependent variables. The method was tested by solving the following problems: the flow over a flat plate, around a circular cylinder, and around a Joukowski airfoil. The last two problems involved massive flow separation. The approach offers the capability of confining the domain of computations to the region where two quantities, the vorticity and the difference in dilatation between the real flow and the potential flow around the body, are non-negligible.

Elrefaee, M. M.↗