The slow recirculating flow near the rear stagnation point of a wake

A model is suggested in which some of the important features of the circulating flow inside the two-dimensional near wake are derived by assuming a slow viscous flow. The theory considers the flow away from the body base. It is found that there is a region of constant speed merging, as we go downstream, into a region of stagnation-apex flow. The velocity returning from the rear stagnation point along the center streamline is shown to be a slowly varying function of the 'wedge-angle,' of the wake and to be roughly one half the velocity at the edge of the shear layers driving the wake-cavity flow. These results seem to be in agreement with experimental data

eCommerce Market Convergence in Action: Social Casinos and Real Money Gambling

The social casino and real money gambling industries, including gambling at online and live venues (such as casino resorts), are quickly converging (H2 Gambling Capital & Odobo, 2013). Differences in demographics and gambling behaviors for different frequencies of social casino participation among real money online gamblers are examined to explore customer behaviors between the two markets. Frequency of play in social casino games varied depending on gender and education, similar to patterns in real money gambling. Players who participated more frequently in social casino games were also more likely to spend more time participating in real money online gambling, suggested to be due to increased familiarity with the games. Findings provide consumer insight for online gambling and social casino companies working toward convergence of the two game types, including implications for target markets for crossover play, loyalty programs, and corporate social responsibility

Compact high order schemes for the Euler equations

An implicit approximate factorization (AF) algorithm is constructed which has the following characteistics. In 2-D: The scheme is unconditionally stable, has a 3 x 3 stencil and at steady state has a fourth order spatial accuracy. The temporal evolution is time accurate either to first or second order through choice of parameter. In 3-D: The scheme has almost the same properties as in 2-D except that it is now only conditionally stable, with the stability condition (the CFL number) being dependent on the cell aspect ratios, delta y/delta x and delta z/delta x. The stencil is still compact and fourth order accuracy at steady state is maintained. Numerical experiments on a 2-D shock-reflection problem show the expected improvement over lower order schemes, not only in accuracy (measured by the L sub 2 error) but also in the dispersion. It is also shown how the same technique is immediately extendable to Runge-Kutta type schemes resulting in improved stability in addition to the enhanced accuracy

Spurious frequencies as a result of numerical boundary treatments

The stability theory for finite difference Initial Boundary-Value approximations to systems of hyperbolic partial differential equations states that the exclusion of eigenvalues and generalized eigenvalues is a sufficient condition for stability. The theory, however, does not discuss the nature of numerical approximations in the presence of such eigenvalues. In fact, as was shown previously, for the problem of vortex shedding by a 2-D cylinder in subsonic flow, stating boundary conditions in terms of the primitive (non-characteristic) variables may lead to such eigenvalues, causing perturbations that decay slowly in space and remain periodic time. Characteristic formulation of the boundary conditions avoided this problem. A more systematic study of the behavior of the (linearized) one-dimensional gas dynamic equations under various sets of oscillation-inducing legal boundary conditions is reported

Splitting methods for low Mach number Euler and Navier-Stokes equations

Examined are some splitting techniques for low Mach number Euler flows. Shortcomings of some of the proposed methods are pointed out and an explanation for their inadequacy suggested. A symmetric splitting for both the Euler and Navier-Stokes equations is then presented which removes the stiffness of these equations when the Mach number is small. The splitting is shown to be stable