Volume 34, Issue 2

The influence of thermal motion of electrons on the processes of relativistic plasma oscillations is studied analytically and numerically. It is shown that if the temperature of electrons grows and exceeds a certain critical level, then the breaking effect vanishes due to transformation of plasma oscillations into travelling waves. Analytical conclusions are made in the framework of the theory of small perturbations based on Lagrangian variables. Numerical simulation of the transformation is performed using three different algorithms constructed on the basis of the method of finite differences in Eulerian variables. The analytical results are in good agreement with numerical experiments.

We investigate a numerical solution method for a degenerate parabolic variational inequality that determines American vanilla put pricing. This method is based on piecewise linear finite elements in spatial variables and the backward Euler finite difference in time variable. For the approximate solution, we get sharp error estimate of order O ( h + τ 3/4 ) in the energy norm of the corresponding differential operator.

The paper presents results of numerical studies of stochastic properties of time series of the enthalpy of humid air and the heat index characterizing the heat content and thermal effects of humid air on human beings. The study was based on real meteorological observations and stochastic model of joint time series for surface air temperature and relative humidity taking into account daily course of real meteorological processes.

Basic properties of some finite difference schemes for two-dimensional nonlinear dispersive equations for hydrodynamics of surface waves are considered. It is shown that stability conditions for difference schemes of shallow water equations are qualitatively different in the cases the dispersion is taken into account, or not. The difference in the behavior of phase errors in one- and two-dimensional cases is pointed out. Special attention is paid to the numerical algorithm based on the splitting of the original system of equations into a nonlinear hyperbolic system and a scalar linear equation of elliptic type.

The paper presents the results of direct numerical simulation of turbulent plane Couette flow. The calculations were performed for Reynolds numbers Re = U 0 H / ν ( H is the height of the channel, ± U 0 /2 is the motion velocities of the lower and upper walls, respectively, ν is the kinematic viscosity) from 5200 (where viscous effects significantly affect the flow structure) to 80000 (where a logarithmic layer is clearly observed). Estimates of terms of the equation for the balance of turbulent Reynolds stresses are obtained, which indicate the importance of the kinetic energy transport by velocity fluctuations. The vertical transport of the turbulent momentum flux is less important and partly compensated by the transport of pressure fluctuations. It is shown that in the logarithmic layer the normal components of the ‘pressure–strain rate’ correlation tensor are described in the framework of the ‘isotropization of production’ model, and in the central part of the channel they are described by the linear Rotta model [29]. The additive model considering both the interaction of the velocity field fluctuation and the influence of the mean velocity gradient is a good approximation only for the off-diagonal component of the tensor entering the balance equation for the turbulent momentum flux.