5,361 research outputs found
Decoupling Techniques for Coupled PDE Models in Fluid Dynamics
We review decoupling techniques for coupled PDE models in fluid dynamics. In particular, we are interested in the coupled models for fluid flow interacting with porous media flow and the fluid structure interaction (FSI) models. For coupled models for fluid flow interacting with porous media flow, we present decoupled preconditioning techniques, two-level and multilevel methods, Newton-type linearization-based two-level and multilevel algorithms, and partitioned time-stepping methods. The main theory and some numerical experiments are given to illustrate the effectiveness and efficiency of these methods. For the FSI models, partitioned time-stepping algorithms and a multirate time-stepping algorithm are carefully studied and analyzed. Numerical experiments are presented to highlight the advantages of these methods
Zonal Flow Magnetic Field Interaction in the Semi-Conducting Region of Giant Planets
All four giant planets in the Solar System feature zonal flows on the order
of 100 m/s in the cloud deck, and large-scale intrinsic magnetic fields on the
order of 1 Gauss near the surface. The vertical structure of the zonal flows
remains obscure. The end-member scenarios are shallow flows confined in the
radiative atmosphere and deep flows throughout the entire planet. The
electrical conductivity increases rapidly yet smoothly as a function of depth
inside Jupiter and Saturn. Deep zonal flows will inevitably interact with the
magnetic field, at depth with even modest electrical conductivity. Here we
investigate the interaction between zonal flows and magnetic fields in the
semi-conducting region of giant planets. Employing mean-field electrodynamics,
we show that the interaction will generate detectable poloidal magnetic field
perturbations spatially correlated with the deep zonal flows. Assuming the peak
amplitude of the dynamo alpha-effect to be 0.1 mm/s, deep zonal flows on the
order of 0.1 - 1 m/s in the semi-conducting region of Jupiter and Saturn would
generate poloidal magnetic perturbations on the order of 0.01% - 1% of the
background dipole field. These poloidal perturbations should be detectable with
the in-situ magnetic field measurements from the Juno mission and the Cassini
Grand Finale. This implies that magnetic field measurements can be employed to
constrain the properties of deep zonal flows in the semi-conducting region of
giant planets.Comment: 38 pages, 12 figures, revised submission to Icaru
Growth, competition and cooperation in spatial population genetics
We study an individual based model describing competition in space between
two different alleles. Although the model is similar in spirit to classic
models of spatial population genetics such as the stepping stone model, here
however space is continuous and the total density of competing individuals
fluctuates due to demographic stochasticity. By means of analytics and
numerical simulations, we study the behavior of fixation probabilities,
fixation times, and heterozygosity, in a neutral setting and in cases where the
two species can compete or cooperate. By concluding with examples in which
individuals are transported by fluid flows, we argue that this model is a
natural choice to describe competition in marine environments.Comment: 29 pages, 14 figures; revised version including a section with
results in the presence of fluid flow
Flapping states of an el astically anchored wing in a uniform flow
Linear stability analysis of an elastically anchored wing in a uniform flow
is investigated both analytically and numerically. The analytical formulation
explicitly takes into account the effect of the wake on the wing by means of
Theodorsen's theory. Three different parameters non-trivially rule the observed
dynamics: mass density ratio between wing and fluid, spring elastic constant
and distance between the wing center of mass and the spring anchor point on the
wing. We found relationships between these parameters which rule the transition
between stable equilibrium and fluttering. The shape of the resulting marginal
curve has been successfully verified by high Reynolds number direct numerical
simulations. Our findings are of interest in applications related to energy
harvesting by fluid-structure interaction, a problem which has recently
attracted a great deal of attention. The main aim in that context is to
identify the optimal physical/geometrical system configuration leading to large
sustained motion, which is the source of energy we aim to extract.Comment: 10 pages, 11 figures, submitted to J. Fluid. Mec
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