Abstract: Different numerical methods are employed and developed for simulating interfacial flows. A large range of applications belong to this group, e.g. two-phase flows of air bubbles in water or water drops in air. In such problems surface tension effects often play a dominant role. In this paper, various models of surface tension force for interfacial flows, the CSF, CSS, PCIL and SGIP models have been applied to simulate the motion of small air bubbles in water and the results were compared and reviewed. It has been pointed out that by using SGIP or PCIL models, we are able to simulate bubble rise and obtain results in close agreement with the experimental data.
Abstract: In this paper, the two-dimensional stagger grid
interface pressure (SGIP) model has been generalized and presented
into three-dimensional form. For this purpose, various models of
surface tension force for interfacial flows have been investigated and
compared with each other. The VOF method has been used for
tracking the interface. To show the ability of the SGIP model for
three-dimensional flows in comparison with other models, pressure
contours, maximum spurious velocities, norm spurious flow
velocities and pressure jump error for motionless drop of liquid and
bubble of gas are calculated using different models. It has been
pointed out that SGIP model in comparison with the CSF, CSS and
PCIL models produces the least maximum and norm spurious
velocities. Additionally, the new model produces more accurate
results in calculating the pressure jumps across the interface for
motionless drop of liquid and bubble of gas which is generated in
surface tension force.
Abstract: In the recent past Learning Classifier Systems have
been successfully used for data mining. Learning Classifier System
(LCS) is basically a machine learning technique which combines
evolutionary computing, reinforcement learning, supervised or
unsupervised learning and heuristics to produce adaptive systems. A
LCS learns by interacting with an environment from which it
receives feedback in the form of numerical reward. Learning is
achieved by trying to maximize the amount of reward received. All
LCSs models more or less, comprise four main components; a finite
population of condition–action rules, called classifiers; the
performance component, which governs the interaction with the
environment; the credit assignment component, which distributes the
reward received from the environment to the classifiers accountable
for the rewards obtained; the discovery component, which is
responsible for discovering better rules and improving existing ones
through a genetic algorithm. The concatenate of the production rules
in the LCS form the genotype, and therefore the GA should operate
on a population of classifier systems. This approach is known as the
'Pittsburgh' Classifier Systems. Other LCS that perform their GA at
the rule level within a population are known as 'Mitchigan' Classifier
Systems. The most predominant representation of the discovered
knowledge is the standard production rules (PRs) in the form of IF P
THEN D. The PRs, however, are unable to handle exceptions and do
not exhibit variable precision. The Censored Production Rules
(CPRs), an extension of PRs, were proposed by Michalski and
Winston that exhibit variable precision and supports an efficient
mechanism for handling exceptions. A CPR is an augmented
production rule of the form: IF P THEN D UNLESS C, where
Censor C is an exception to the rule. Such rules are employed in
situations, in which conditional statement IF P THEN D holds
frequently and the assertion C holds rarely. By using a rule of this
type we are free to ignore the exception conditions, when the
resources needed to establish its presence are tight or there is simply
no information available as to whether it holds or not. Thus, the IF P
THEN D part of CPR expresses important information, while the
UNLESS C part acts only as a switch and changes the polarity of D
to ~D. In this paper Pittsburgh style LCSs approach is used for
automated discovery of CPRs. An appropriate encoding scheme is
suggested to represent a chromosome consisting of fixed size set of
CPRs. Suitable genetic operators are designed for the set of CPRs
and individual CPRs and also appropriate fitness function is proposed
that incorporates basic constraints on CPR. Experimental results are
presented to demonstrate the performance of the proposed learning
classifier system.