Voltzinger N. E., Androsov A. A., Klevannyy K. A., Safrai A. S.
Results devoted to different aspects of oceanographic models for non-hydrostatic dynamics reported during two-three last decades are discussed in this review. Achievement in this field was obtained mainly due to the progress in computational hydrodynamics which marked a qualitatively new current level of World ocean dynamics and its regions modelling. Wide thematic of non-hydrostatic modelling includes consideration of the processes and phenomena with pronounced vertical movements. For their description, taking into account the dynamic component of pressure is desirable and in some cases essential. Statement of particular boundary value problems for non-hydrostatic dynamics equations subsystems, methods of their realization and, finally, evaluation and analysis of non-hydrostatic effects are the objectives of the present review. The basis of oceanographic non-hydrostatic models consists in formulation and methods of resolving of boundary problems for the Navier—Stokes equations of viscous incompressible fluid dynamics. A necessary consideration of such works is a section of this review. The presentation focuses at works which use the most common projections method of oceanographic models realization by different types of domain discretization: finite-difference grid, finite-volume, finiteelement and different forms of solution presentation: in boundary conformal coordinates, series, spectral decomposition etc. These approximations are tested and used for separate mesoscale processes and non-hydrostatic dynamics of subdomain of the region in the frame of a large-scale model. The structure of the projection method determines the splitting operator of the task and computation of the velocity fields approach at stages of time step. The hydrostatic problem solution can serve as such an approach. Such a suitable approach links hydrostatic approach with a non-hydrostatic module for the Navier—Stokes equations. That is emphasized in this review.
This review is brief. We tried not to overload it either with formulas, where it was possible, or bibliography because each cited reference in general contains its own wide bibliography. Its goal is presentation in a simple and general view of the status of matured non-hydrostatic modelling which elements will in the near future make it possible to resolve boundary problems of non-hydrostatic dynamics of wide regions and longest section of World ocean shelf on the basis of parallel computing.