26,745 research outputs found
The role of long waves in the stability of the plane wake
This work is directed towards investigating the fate of three-dimensional
long perturbation waves in a plane incompressible wake. The analysis is posed
as an initial-value problem in space. More specifically, input is made at an
initial location in the downstream direction and then tracing the resulting
behavior further downstream subject to the restriction of finite kinetic
energy. This presentation follows the outline given by Criminale and Drazin
[Stud. in Applied Math. \textbf{83}, 123 (1990)] that describes the system in
terms of perturbation vorticity and velocity. The analysis is based on large
scale waves and expansions using multi scales and multi times for the partial
differential equations. The multiscaling is based on an approach where the
small parameter is linked to the perturbation property independently from the
flow control parameter. Solutions of the perturbative equations are determined
numerically after the introduction of a regular perturbation scheme
analytically deduced up to the second order. Numerically, the complete linear
system is also integrated. Since the results relevant to the complete problem
are in very good agreement with the results of the first order analysis, the
numerical solution at the second order was deemed not necessary. The use for an
arbitrary initial-value problem will be shown to contain a wealth of
information for the different transient behaviors associated to the symmetry,
angle of obliquity and spatial decay of the long waves. The amplification
factor of transversal perturbations never presents the trend - a growth
followed by a long damping - usually seen in waves with wavenumber of order one
or less. Asymptotical instability is always observed.Comment: accepted Physical Review E, March 201
Spatial Manifestations of Order Reduction in Runge-Kutta Methods for Initial Boundary Value Problems
This paper studies the spatial manifestations of order reduction that occur
when time-stepping initial-boundary-value problems (IBVPs) with high-order
Runge-Kutta methods. For such IBVPs, geometric structures arise that do not
have an analog in ODE IVPs: boundary layers appear, induced by a mismatch
between the approximation error in the interior and at the boundaries. To
understand those boundary layers, an analysis of the modes of the numerical
scheme is conducted, which explains under which circumstances boundary layers
persist over many time steps. Based on this, two remedies to order reduction
are studied: first, a new condition on the Butcher tableau, called weak stage
order, that is compatible with diagonally implicit Runge-Kutta schemes; and
second, the impact of modified boundary conditions on the boundary layer theory
is analyzed.Comment: 41 pages, 9 figure
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Instabilities in free-surface electroosmotic flows
This paper was presented at the 2nd Micro and Nano Flows Conference (MNF2009), which was held at Brunel University, West London, UK. The conference was organised by Brunel University and supported by the Institution of Mechanical Engineers, IPEM, the Italian Union of Thermofluid dynamics, the Process Intensification Network, HEXAG - the Heat Exchange Action Group and the Institute of Mathematics and its Applications.With the recent development of novel microfluidic devices electroosmotic flows with fluid/fluid interfaces have emerged as very important subjects of investigation. Two immiscible fluids may need to be
transported in a microchannel, or one side of a channel may be open to air for various purposes, including adsorption of airborne molecules to liquid for high-sensitivity substance detection. The liquid/liquid or
liquid/gas interface in these cases can deform, resulting in significant corrugations followed sometimes by incipient rupture of liquid layers. For electroosmotic flow the rupture, leading to shortcircuit, can cause overall failure of the device. It is thus imperative to know the conditions for the rupture as well as the initial interfacial instability. Studies based on the Debye-Huckle approximation reveal that all free-surface electroosmotic flows of thickness larger than the Debye screening length are unstable and selectively lead to
rupture. Layers of the order of Debye screening length, however, are not properly described by the Debye-Huckle approximation. Even for micro-scale layers, the rupture phenomenon can make local layer
thickness to be nanoscale. A fully coupled system of hydrodynamics, electric field, and ionic distribution need to be analyzed. In this paper linear instability and subsequent nonlinear developments of a nanoscale free-surface electroosmotic flow are reported.This study is sponsored by the Ministry of Education, Science and Technology of Korea through the World Class University Grant
Parareal in time 3D numerical solver for the LWR Benchmark neutron diffusion transient model
We present a parareal in time algorithm for the simulation of neutron
diffusion transient model. The method is made efficient by means of a coarse
solver defined with large time steps and steady control rods model. Using
finite element for the space discretization, our implementation provides a good
scalability of the algorithm. Numerical results show the efficiency of the
parareal method on large light water reactor transient model corresponding to
the Langenbuch-Maurer-Werner (LMW) benchmark [1]
Stability analysis of non-autonomous reaction-diffusion systems: the effects of growing domains
By using asymptotic theory, we generalise the Turing diffusively-driven instability conditions for reaction-diffusion systems with slow, isotropic domain growth. There are two fundamental biological differences between the Turing conditions on fixed and growing domains, namely: (i) we need not enforce cross nor pure kinetic conditions and (ii) the restriction to activator-inhibitor kinetics to induce pattern formation on a growing biological system is no longer a requirement. Our theoretical findings are confirmed and reinforced by numerical simulations for the special cases of isotropic linear, exponential and logistic growth profiles. In particular we illustrate an example of a reaction-diffusion system which cannot exhibit a diffusively-driven instability on a fixed domain but is unstable in the presence of slow growth
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