Preconditioned iterative methods for coupled discretizations of fluid flow problems

Computational fluid dynamics, where simulations require largecomputation times, is one of the areas of application of highperformance computing. Schemes such as the SIMPLE (semi-implicitmethod for pressure-linked equations) algorithm are often usedto solve the discrete Navier-Stokes equations. Generally theseschemes take a short time per iteration but require a largenumber of iterations. For simple geometries (or coarser grids)the overall CPU time is small. However, for finer grids or morecomplex geometries the increase in the number of iterationsmay be a drawback and the decoupling of the differential equationsinvolved implies a slow convergence of rotationally dominatedproblems that can be very time consuming for realistic applications.So we analyze here another approach, DIRECTO, that solves theequations in a coupled way. With recent advances in hardwaretechnology and software design, it became possible to solvecoupled Navier-Stokes systems, which are more robust but implyincreasing computational requirements (both in terms of memoryand CPU time). Two approaches are described here (band blockLU factorization and preconditioned GMRES) for the linear solverrequired by the DIRECTO algorithm that solves the fluid flowequations as a coupled system. Comparisons of the effectivenessof incomplete factorization preconditioners applied to the GMRES(generalized minimum residual) method are shown. Some numericalresults are presented showing that it is possible to minimizeconsiderably the CPU time of the coupled approach so that itcan be faster than the decoupled one.     

Simulations of large acoustic scintillations in the straits of Florida

Using a full-wave acoustic model, Monte Carlo numerical studies of intensity fluctuations in a realistic shallow water environment that simulates the Straits of Florida, including internal wave fluctuations and bottom roughness, have been performed. Results show that the sound intensity at distant receivers scintillates dramatically. The acoustic scintillation index SI increases rapidly with propagation range and is significantly greater than unity at ranges beyond about 10 km. This result supports a theoretical prediction by one of the authors. Statistical analyses show that the distribution of intensity of the random wave field saturates to the expected Rayleigh distribution with SI= 1 at short range due to multipath interference effects, and then SI continues to increase to large values. This effect, which is denoted supersaturation, is universal at long ranges in waveguides having lossy boundaries (where there is differential mode attenuation). The intensity distribution approaches a log-normal distribution to an excellent approximation; it may not be a universal distribution and comparison is also made to a K distribution. The long tails of the log-normal distribution cause "acoustic intermittency" in which very high, but rare, intensities occur.     

Study of horizontal multipaths and ray chaos due to ocean mesoscale structure

Long-range ocean acoustic propagation in the presence of idealized mesoscale structure is studied by first deriving a two-dimensional horizontal-plane parabolic wave equation that follows from the adiabatic mode approximation. In the geometric limit, a nonautonomous Hamiltonian dynamical system having one degree of freedom is derived. A stochastic formalism is developed to analyze this nonintegrable dynamical system. The main result is that on average two rays that are initially separated by an infinitesimal amount diverge exponentially at a rate given by the Lyapunov exponent that has been calculated theoretically and compared to numerical experiments with agreement to two decimal places. The practical implication of this result is that tomographic inversions based on assumed pointwise accurate ray predictions might not be possible beyond the "predictability horizon" of many thousands of kilometers, due to horizontal-plane multipaths induced by naturally occurring mesoscale activity.     

Synthesis and properties of mullite and cordierite aerogels

This work deals with the preparation of aluminosilicate aerogels, especially mullite (3Al₂O₃·2SiO₂) and cordierite (2MgO·2Al₂O₃·5SiO₂) aerogels, from the cohydrolysis of tetraethoxysilane and chelated aluminum-secbutylate; in the case of cordierite magnesium nitrate was added. The influence of various preparation conditions on the aerogel synthesis is described. Crystallization and sintering behavior of mullite aerogels supercritically dried in acetone or alcohol differs from that one of mullite aerogels dried in CO₂. During non-isothermal heat treatment the former show a drastically reduced shrinkage compared to the latter. This behavior can be explained by a phase separation during the high temperature autoclaving process. In cordierite aerogels the crystallization of tetragonal mullite at about 1000°C is observed, while the correspondent xerogels show the crystallization of - and - cordierite between 1000 and 1100°C. On the other hand sintering is promoted in cordierite aerogels, which is due to the content of MgO.     

Study of a novel range-dependent propagation effect with application to the axial injection of signals from the Kaneohe source

A novel range-dependent propagation effect occurs when a source is placed on the seafloor in shallow water with a downward refracting sound speed profile, and sound waves propagate down a slope into deep water. Under these conditions, small grazing-angle sound waves slide along the bottom downward and outward from the source until they reach the depth of the sound channel axis in deep water, where they are detached from the sloping bottom and continue to propagate outward near the sound channel axis. This "mudslide" effect is one of a few robust and predictable acoustic propagation effects that occur in range-dependent ocean environments. As a consequence of this effect, a bottom mounted source in shallow water can inject a significant amount of acoustic energy into the axis of the deep ocean sound channel that can then propagate to very long ranges. Numerical simulations with a full-wave range-dependent acoustic model show that the Kaneohe experiment had the appropriate source, bathymetry, and sound speed profiles that allows this effect to operate efficiently. This supports the interpretation that some of the near-axial acoustic signals, received near the coast of California from the bottom mounted source located in shallow water in Kaneohe Bay, Oahu, Hawaii, were injected into the sound channel of the deep Pacific Ocean by this mechanism. Numerical simulations suggest that the mudslide effect is robust.     

Theory of explosive beam spreading due to ray chaos

In an ocean acoustic situation where rays are known to be chaotic, a theory based on a Gaussian beam approximation is used to show that the width of a narrow-angle beam increases exponentially (explosively) with range at a rate that is given by the Lyapunov exponent that is calculated in the geometric limit. This finite frequency result shows that the phenomenon of "wave chaos" is real, and might be observable experimentally.