On Pattern Selection in Three-Dimensional Bénard-Marangoni Flows

2012 ◽  
Vol 11 (3) ◽  
pp. 893-924 ◽  
Author(s):  
Arne Morten Kvarving ◽  
Tormod Bjøntegaard ◽  
Einar M. Rønquist
Keyword(s):  
Numerical Experiments ◽  
Initial Conditions ◽  
Computational Study ◽  
Fluid Layer ◽  
Three Dimensional ◽  
Fixed Number ◽  
Random Initial Condition ◽  
Initial Condition ◽  
Convection Pattern ◽  
Number Of Cells

AbstractIn this paper we study Bénard-Marangoni convection in confined containers where a thin fluid layer is heated from below. We consider containers with circular, square and hexagonal cross-sections. For Marangoni numbers close to the critical Marangoni number, the flow patterns are dominated by the appearance of the well-known hexagonal convection cells. The main purpose of this computational study is to explore the possible patterns the system may end up in for a given set of parameters. In a series of numerical experiments, the coupled fluid-thermal system is started with a zero initial condition for the velocity and a random initial condition for the temperature. For a given set of parameters we demonstrate that the system can end up in more than one state. For example, the final state of the system may be dominated by a steady convection pattern with a fixed number of cells, however, the same system may occasionally end up in a steady pattern involving a slightly different number of cells, or it may end up in a state where most of the cells are stationary, while one or more cells end up in an oscillatory state. For larger aspect ratio containers, we are also able to reproduce dislocations in the convection pattern, which have also been observed experimentally. It has been conjectured that such imperfections (e.g., a localized star-like pattern) are due to small irregularities in the experimental setup (e.g., the geometry of the container). However, we show, through controlled numerical experiments, that such phenomena may appear under otherwise ideal conditions. By repeating the numerical experiments for the same non-dimensional numbers, using a different random initial condition for the temperature in each case, we are able to get an indication of how rare such events are. Next, we study the effect of symmetrizing the initial conditions. Finally, we study the effect of selected geometry deformations on the resulting convection patterns.

Computational Studies on Charge Stratification and Fuel-Air Mixing in a New Two-Stroke Engine

2005 ◽  
Author(s):  
Shamit Bakshi ◽  
T. N. C. Anand ◽  
R. V. Ravikrishna
Keyword(s):  
Initial Conditions ◽  
Computational Study ◽  
Three Dimensional ◽  
The State ◽  
Operating Conditions ◽  
Injection System ◽  
Critical Parameters ◽  
Mixing Process ◽  
Air Mixing ◽  
Stroke Engine

In this paper, detailed computational study is presented which helps to understand and improve the fuel-air mixing in a new direct-mixture-injection two-stroke engine. This new air-assisted injection system-based two-stroke engine is being developed at the Indian Institute of Science, Bangalore over the past few years. It shows the potential to meet emission norms such as EURO-II and EURO-III and also deliver satisfactory performance. This work proposes a comprehensive strategy to study the air-fuel mixing process in this engine and shows that this strategy can be potentially used to improve the engine performance. A three-dimensional compressible flow code with standard k–ε turbulence model with wall functions is developed and used for this modeling. To account for the moving boundary or piston in the engine cylinder domain, a non-stationary and deforming grid is used in this region with stationary cells in the ports and connecting ducts. A flux conservation scheme is used in the domain interface to allow the in-cylinder moving mesh to slide past the fixed port meshes. The initial conditions for flow parameters are taken from the output of a three-dimensional scavenging simulation. The state of the inlet charge is obtained from a separate modeling of the air-assisted injection system of this engine. The simulation results show that a large, near-stoichiometric region is present at most operating conditions in the cylinder head plane. The state of the in-cylinder charge at the onset of ignition is studied leading to a good understanding of the mixing process. In addition, sensitivity of two critical parameters on the mixing and stratification is investigated. The suggested parameters substantially enhance the flammable proportion at the onset of combustion. The predicted P–θ from a combustion simulation supports this recommendation.

scholarly journals N-ORDER MOMENT FUNCTION FOR THE SOLUTION OF THE CAUCHY PROBLEM FOR DIFFUSION EQUATION WITH RANDOM COEFFICIENTS

2017 ◽  
Vol 17 (8) ◽  
pp. 5-20
Author(s):  
T.V. Besedina
Keyword(s):  
Cauchy Problem ◽  
Diffusion Equation ◽  
Three Dimensional ◽  
Random Coefficients ◽  
Moment Function ◽  
Order Moment ◽  
Random Initial Condition ◽  
Initial Condition ◽  
Dimensional Diffusion ◽  
The Cauchy Problem

Formula for n-order moment function for the solution of the Cauchy problem for three-dimensional diffusion equation with random coefficients and random initial condition is derived.

ON THE GROSS–PITAEVSKII EQUATION WITH STRONGLY ANISOTROPIC CONFINEMENT: FORMAL ASYMPTOTICS AND NUMERICAL EXPERIMENTS

2005 ◽  
Vol 15 (05) ◽  
pp. 767-782 ◽  
Author(s):  
WEIZHU BAO ◽  
PETER A. MARKOWICH ◽  
CHRISTIAN SCHMEISER ◽  
RADA M. WEISHÄUPL
Keyword(s):  
Asymptotic Approximation ◽  
Numerical Experiments ◽  
Three Dimensional ◽  
Approximation Error ◽  
Fixed Number ◽  
Pitaevskii Equation ◽  
Strongly Coupled ◽  
Confining Potential ◽  
Formal Asymptotics ◽  
Formal Limit

The three-dimensional (3D) Gross–Pitaevskii equation with strongly anisotropic confining potential is analyzed. The formal limit as the ratio of the frequencies ε tends to zero provides a denumerable system of two-dimensional Gross–Pitaevskii equations, strongly coupled through the cubic nonlinearities. To numerically solve the asymptotic approximation only a finite number of limiting equations is considered. Finally, the approximation error for a fixed number of equations is compared for different ε tending to zero. On the other hand, the approximation error for an increasing number of terms in the approximation is observed.

scholarly journals On the emergence of random initial conditions in fluid limits

2016 ◽  
Vol 53 (4) ◽  
pp. 1193-1205 ◽  
Author(s):  
A. D. Barbour ◽  
P. Chigansky ◽  
F. C. Klebaner
Keyword(s):  
Carrying Capacity ◽  
Classical Result ◽  
Initial Conditions ◽  
Death Process ◽  
Initial Population ◽  
Random Initial Condition ◽  
Initial Condition ◽  
Birth And Death Process ◽  
Fluid Limit ◽  
Random Initial Conditions

Abstract In the paper we present a phenomenon occurring in population processes that start near 0 and have large carrying capacity. By the classical result of Kurtz (1970), such processes, normalized by the carrying capacity, converge on finite intervals to the solutions of ordinary differential equations, also known as the fluid limit. When the initial population is small relative to the carrying capacity, this limit is trivial. Here we show that, viewed at suitably chosen times increasing to ∞, the process converges to the fluid limit, governed by the same dynamics, but with a random initial condition. This random initial condition is related to the martingale limit of an associated linear birth-and-death process.

scholarly journals Flux Separation in Photospheric Magnetoconvection

2001 ◽  
Vol 203 ◽  
pp. 219-221 ◽  
Author(s):  
N. O. Weiss ◽  
M. R. E. Proctor
Keyword(s):  
Magnetic Field ◽  
Magnetic Flux ◽  
Numerical Experiments ◽  
Large Scale ◽  
Initial Conditions ◽  
Three Dimensional ◽  
Small Scale ◽  
The Sun ◽  
Intermediate Regime ◽  
Magnetic Features

Numerical experiments on three-dimensional magnetoconvection in a stratified compressible layer reveal a range of different patterns, depending on the strength of the imposed magnetic field. As the field is decreased there is a transition from small-scale plumes, in the magnetically dominated regime, to large-scale vigorous plumes when the field is dominated by the motion. In the intermediate regime magnetic flux separates from the motion, so that there are almost field-free regions, with clusters of vigorous plumes, surrounded by regions where the Lorentz force is strong enough to control the dynamics. There is a range of field strengths where either small-scale plumes or flux-separated solutions can persist, depending on initial conditions for the computation. These results can be related to magnetic features at the surface of the Sun.

Numerical experiments in boundary-layer stability

1984 ◽  
Vol 392 (1803) ◽  
pp. 373-389 ◽  
Keyword(s):  
Boundary Layer ◽  
Numerical Experiments ◽  
Stokes Equations ◽  
Initial Conditions ◽  
Three Dimensional ◽  
Plate Boundary ◽  
Navier Stokes ◽  
Boundary Layer Stability ◽  
Physical Processes ◽  
Navier Stokes Equations

Numerical solution of the three-dimensional incompressible Navier-Stokes equations is used to study the instability of a flat-plate boundary layer in a manner analogous to the vibrating-ribbon experiments. Flow field structures are observed which are very similar to those found in the vibrating-ribbon experiment to which computational initial conditions have been matched. Stream wise periodicity is assumed in the simulation so that the evolution occurs in time, but the events that constitute the instability are so similar to the spatially occurring ones of the laboratory that it seems clear the physical processes involved are the same. A spectral and finite difference numerical algorithm is employed in the simulation.

Tension of organizing filaments of scroll waves

1994 ◽  
Vol 347 (1685) ◽  
pp. 611-630 ◽  
Keyword(s):  
Evolution Equation ◽  
Numerical Experiments ◽  
Asymptotic Theory ◽  
Initial Conditions ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Filament Length ◽  
Monotonic Change ◽  
Scroll Wave ◽  
Scroll Waves

We consider the asymptotic theory for the dynamics of organizing filaments of three-dimensional scroll waves. For a generic autowave medium where two dimensional vortices do not meander, we show that some of the coefficients of the evolution equation are always zero. This simpler evolution equation predicts a monotonic change of the total filament length with time, independently of initial conditions. Whether the filament will shrink or expand is determined by a single coefficient, the filament tension, that depends on the medium parameters. We illustrate the behaviour of scroll wave filaments with positive and negative tension by numerical experiments. In particular, we show that in the case of negative filament tension, the straight filament is unstable, and its evolution may lead to a multiplication of vortices.

Heat Conduction in Solids With Random Initial Conditions

1974 ◽  
Vol 96 (4) ◽  
pp. 474-477 ◽  
Author(s):  
G. Ahmadi
Keyword(s):  
Temperature Field ◽  
Heat Conduction ◽  
General Theory ◽  
Unbounded Domain ◽  
Initial Conditions ◽  
Bounded Domains ◽  
Random Initial Condition ◽  
Initial Condition ◽  
Random Initial Conditions ◽  
Random Temperature Field

The problem of heat conduction in solids with random initial condition is studied. A general theory is first discussed and several examples are considered. It is observed that the homogeneity of the random initial condition is sufficient for the homogeneity of the temperature field in an unbounded domain. But in bounded domains the random temperature field becomes nonhomogeneous even though the initial condition is homogeneous.

Steady and oscillatory bimodal convection

1994 ◽  
Vol 271 ◽  
pp. 103-118 ◽  
Author(s):  
R. M. Clever ◽  
F. H. Busse
Keyword(s):  
Fluid Layer ◽  
Three Dimensional ◽  
Convection Pattern ◽  
Numerical Computations ◽  
Spatial Symmetry ◽  
Prandtl Numbers ◽  
Steady Solutions ◽  
The Stability

Steady three-dimensional convection in the form of bimodal cells in a fluid layer heated from below with rigid boundaries is studied through numerical computations for Prandtl numbers in the range 10 [lsim ] P [lsim ] 100. The stability of the steady solutions with respect to disturbances of various symmetries has been analysed. Typically, the range of stable steady bimodal convection is restricted by the transition to oscillatory bimodal convection. The oscillations preserve the spatial symmetry of the steady bimodal convection pattern in the case of high P and higher wavenumbers, but break it in the case of lower P or lower wavenumbers in the range that has been investigated. Some comparisons are made with experimental observations. The transition from bimodal to knot convection has also been studied.

Is it a Right Assumption That B and Ge are Distributed Randomly After Growing a Strained HBT-Structure?

2002 ◽  
Vol 716 ◽  
Author(s):  
Victor I. Kol'dyaev
Keyword(s):  
Surface Segregation ◽  
Initial Conditions ◽  
Initial Condition ◽  
Basic Assumptions ◽  
Transient Diffusion ◽  
Segregation Process ◽  
Main Observation

AbstractIt is accepted that surface Ge atoms are considered to be responsible for the surface B segregation process. A set of original experiments is carried out. A main observation from the B and Ge profiles grown at different conditions shows that at certain conditions B is taking initiative and determine the Ge surface segregation process. basic assumptions are suggested to self-consistently explain these original experimental features and what is observed in the literature. These results have a strong implication for modeling the B diffusion in Si1-xGex where the initial conditions should be formulated accounting for the correlation in B and Ge distribution. A new assumption for the initial condition to be “all B atoms are captured by Ge” is regarded as a right one implicating that there is no any transient diffusion representing the B capturing kinetics.

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