Compact finite difference - Fourier spectral method for three-dimensional incompressible Navier-Stokes equations

A new compact finite difference-Fourier spectral hybrid method for solving the three dimensional incompressible Navier-Stokes equations is developed in the present paper. The fifth-order upwind compact finite difference schemes for the nonlinear convection terms in the physical space, and the sixth-order center compact schemes for the derivatives in spectral space are described, respectively. The fourth-order compact schemes in a single nine-point cell for solving the Helmholtz equations satisfied by the velocities and pressure in spectral space is derived and its preconditioned conjugate gradient iteration method is studied. The treatment of pressure boundary conditions and the three dimensional non-reflecting outflow boundary conditions are presented. Application to the vortex dislocation evolution in a three dimensional wake is also reported.

Upwind compact method and direct numerical-simulation of driven flow in a square cavity

A high-order accurate finite-difference scheme, the upwind compact method, is proposed. The 2-D unsteady incompressible Navier-Stokes equations are solved in primitive variables. The nonlinear convection terms in the governing equations are approximated by using upwind biased compact difference, and other spatial derivative terms are discretized by using the fourth-order compact difference. The upwind compact method is used to solve the driven flow in a square cavity. Solutions are obtained for Reynolds numbers as high as 10000. When Re less than or equal to 5000, the results agree well with those in literature. When Re = 7500 and Re = 10000, there is no convergence to a steady laminar solution, and the flow becomes unsteady and periodic.

Upwind compact scheme with dispersion control for aerodynamic equations

A compact upwind scheme with dispersion control is developed using a dissipation analogy of the dispersion term. The term is important in reducing the unphysical fluctuations in numerical solutions. The scheme depends on three free parameters that may be used to regulate the size of dissipation as well as the size and direction of dispersion. A coefficient to coordinate the dispersion is given. The scheme has high accuracy, the method is simple, and the amount of computation is small. It also has a good capability of capturing shock waves. Numerical experiments are carried out with two-dimensional shock wave reflections and the results are very satisfactory.

Study on the Performance of a Compact Compound Oil/Gas/Water Separator for Offshore Oil Industry

High-efficiency separation of the oil/gas/water mixtures is a significant issue in offshore oil industry. To reduce the total cost by means of reduction in weight and space compared with conventional separators, a novel compact compound oil/gas/water separator is developed. The research works on oil-gas-water separation by compound separating techniques is described in this paper. The innovative separator is a gravity settling tank with helical pipes within and T-shaped pipes outside. Both experiments and numerical simulations are presented to study the separating performance and efficiency of the helical pipes, which are the main part of the separator.

Report on Marine Mammal Unusual Mortality Event UMESE0501Sp: Multispecies Mass Stranding of Pilot Whales (Globicephala macrorhynchus), Minke Whale (Balaenoptera acutorostrata), and Dwarf Sperm Whales (Kogia sima) in North Carolina on 15-16 January 2005

On 15-16 January 2005, three offshore species of cetaceans (33 short-finned pilot whales, Globicephala macrorhynchus, one minke whale, Balaenoptera acutorostrata, and two dwarf sperm whales, Kogia sima) stranded alive on the beaches of North Carolina. The pilot whales stranded near Oregon Inlet, the minke whale in northern North Carolina, and the dwarf sperm whales near Cape Hatteras. Live strandings of three species in one weekend was unique in North Carolina and qualified as an Unusual Mortality Event. Gross necropsies were conducted on 16-17 January 2005 on 27 pilot whales, two dwarf sperm whales, and the minke whale. Samples were collected for clinical pathology, parasitology, gross pathology, histopathology, microbiology and serology. There was variation in the number of animals sampled for each collection type, however, due to carcasses washing off the beach or degradation in carcass condition during the course of the response. Comprehensive histologic examination was conducted on 16 pilot whales, both dwarf sperm whales, and the minke whale. Limited organ or only head tissue suites were obtained from nine pilot whales. Histologic examination of tissues began in February 2005 and concluded in December 2005 when final sampling was concluded. Neither the pilot whales nor dwarf sperm whales were emaciated although none had recently ingested prey in their stomachs. The minke whale was emaciated; it was likely a dependent calf that became separated from the female. Most serum biochemistry abnormalities appear to have resulted from the stranding and indicated deteriorating condition from being on land for an extended period. Three pilot whales had clinical evidence of pre-existing systemic inflammation, which was supported by histopathologic findings. Although gross and histologic lesions involving all organ systems were noted, consistent lesions were not observed across species. Verminous pterygoid sinusitis and healed fishery interactions were seen in pilot whales but neither of these changes were causes of debilitation or death. In three pilot whales and one dwarf sperm whale there was evidence of clinically significant disease in postcranial tissues which led to chronic debilitation. Cardiovascular disease was present in one pilot whale and one dwarf sperm whale; musculoskeletal disease and intra-abdominal granulomas were present in two pilot whales. These lesions were possible, but not definitive, causal factors in the stranding. Remaining lesions were incidental or post-stranding. The minke whale and three of five tested pilot whales had positive morbillivirus titers (≥1:8 with one at >1:256), but there was no histologic evidence of active viral infection. Parasites (nematodes, cestodes, and trematodes) were collected from 26 pilot whales and two dwarf sperm whales. Sites of collection included stomach, nasal/pterygoid, peribullar sinuses, blubber, and abdominal cavity. Parasite species, locations and loads were within normal limits for free-ranging cetaceans and were not considered causative for the stranding event. Gas emboli lesions which were considered consistent with or diagnostic of sonarassociated strandings of beaked whales or small cetaceans were not found in the whales stranded as part of UMESE0501Sp. Twenty-five heads were examined with nine specific anatomic locations of interest: extramandibular fat, intramandibular fat, auditory meatus, peribullar acoustic fat, peribullar soft tissue, peribullar sinus, pterygoid sinus, melon, and brain. The common finding in all examined heads was verminous pterygoid sinusitis. Intramandibular adipose tissue reddening, typically adjacent to the vascular plexus, was observed in some individuals and could represent localized hemorrhage resulting from vascular rete rupture, hypostatic congestion, or erythrocyte rupture during the freeze/thaw cycle. One cetacean had peracute to acute subdural hemorrhage that likely occurred from thrashing on the beach post-stranding, although its occurrence prior to stranding cannot be excluded. Information provided to NMFS by the U.S. Navy indicated routine tactical mid-frequency sonar operations from individual surface vessels over relatively short durations and small spatial scales within the area and time period investigated. No marine mammals were detected by marine mammal observers on operational vessels; standard operating procedure for surface naval vessels operating mid-frequency sonar is the use of trained visual lookouts using high-powered binoculars. Sound propagation modeling using information provided to NMFS indicated that acoustic conditions in the vicinity likely depended heavily on position of the receivers (e.g., range, bearing, depth) relative to that of the sources. Absent explicit information on the location of animals meant that it was not possible to estimate received acoustic exposures from active sonar transmissions. Nonetheless, the event was associated in time and space with naval activity using mid-frequency active sonar. It also had a number of features in common (e.g., the “atypical” distribution of strandings involving multiple offshore species, all stranding alive, and without evidence of common infectious or other disease process) with other sonar-related cetacean mass stranding events. Given that this event was the only stranding of offshore species to occur within a 2-3 day period in the region on record (i.e., a very rare event), and given the occurrence of the event simultaneously in time and space with a naval exercise using active sonar, the association between the naval sonar activity and the location and timing of the event could be a causal rather than a coincidental relationship. However, evidence supporting a definitive association is lacking, and, in particular, there are differences in operational/environmental characteristics between this event and previous events where sonar has apparently played a role in marine mammal strandings. This does not preclude behavorial avoidance of noise exposure. No harmful algal blooms were present along the Atlantic coast south of the Chesapeake Bay during the months prior to the event. Environmental conditions, including strong winds, changes in upwelling- to downwelling-favorable conditions, and gently sloping bathymetry, were consistent with conditions which have been correlated with other mass strandings. In summary, we did not find commonality in gross and histologic lesions that would indicate a single cause for this stranding event. Three pilot whales and one dwarf sperm whale had debilitating conditions identified that could have contributed to stranding, one pilot whale had a debilitating condition (subdural hemorrhage) that could have been present prior to or resulting from stranding. While the pilot and dwarf sperm whale strandings may have had a common cause, the minke whale stranding was probably just coincidental. On the basis of examination of physical evidence in the affected whales, however, we cannot definitively conclude that there was or was not a causal link between anthropogenic sonar activity or environmental conditions (or a combination of these factors) and the strandings. Overall, the cause of UMESE0501Sp in North Carolina is not and likely will not be definitively known. (PDF contains 240 pages)

Fixed Points of Closed and Compact Composite Sequences of Operators and Projectors in a Class of Banach Spaces

Some results on fixed points related to the contractive compositions of bounded operators in a class of complete metric spaces which can be also considered as Banach's spaces are discussed through the paper. The class of composite operators under study can include, in particular, sequences of projection operators under, in general, oblique projective operators. In this paper we are concerned with composite operators which include sequences of pairs of contractive operators involving, in general, oblique projection operators. The results are generalized to sequences of, in general, nonconstant bounded closed operators which can have bounded, closed, and compact limit operators, such that the relevant composite sequences are also compact operators. It is proven that in both cases, Banach contraction principle guarantees the existence of unique fixed points under contractive conditions.