A monotone finite-difference high order accuracy scheme for the 2D convection – diffusion equations

A stable finite-difference scheme is constructed on a minimum stencil of a uniform mesh for a two-dimensional steady-state convection – diffusion equation of a general form; the scheme is theoretically studied and tested. It satisfies the maximum principle and has the fourth order of approximation. The scheme monotonicity is controlled by two regularization parameters introduced into the difference operator. The scheme is focused on solving applied convection – diffusion problems with a developed boundary layer, including gravitational convection, thermomagnetic convection, and diffusion of particles in a magnetic fluid. The scheme is tested on the well-known problem of a high-intensive gravitational convection in a horizontal channel of a square cross-section with a uniform heating from the side. A detailed comparison is performed with the monotone Samarskii scheme of the second order approximation on the sequences of square meshes with the number of partitions from 10 to 1000 on each side of the square domain and over the entire range of the Rayleigh numbers, corresponding to the laminar convection mode. A significant advantage of the fourth order scheme in the convergence rate is shown for the decreasing mesh step.

Specialty of vertical water exchange of the Caspian sea on the basis of distribution of transient tracers

The analysis of the reliability of different scenarios for the formation of the vertical structure of the waters of the Caspian Sea, obtained from the distribution of transient tracers (CFC-11, CFC-12, 3H and 3He) at the deep-water stations of the Middle and Southern Caspian within the framework of international integrated isotope-geochemical studies during the maximum sea level rise in 1995–1996. Taking into account the available hydrometeorological data and the characteristics of water dating using transient tracers, it was concluded that after large-scale gravitational convection in the Middle Caspian caused by anomalous cooling of surface waters in the Northern Caspian at the end of the winter of 1976, a structure of water masses was formed that excluded deep water ventilation in the Middle and South Caspian Sea until the mid-90s.