Andrei Bourchtein

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This study concerns some problems of generation of orthogonal grids. The use of scaled Laplace equations is analyzed and the problems related to their application are discussed. The issues of existence and orthogonality of mappings are studied and some analytical examples showing inconsistency of scaled Laplace equations with orthogonality requirements are(More)
A simple geometric condition that defines the class of classical (stereographic, conic and cylindrical) conformal mappings from a sphere onto a plane is derived. The problem of optimization of computational grid for spherical domains is solved in an entire class of conformal mappings on spherical (geodesic) disk. The characteristics of computational grids(More)
Criterions of ellipticity of nonlinear normal mode initialization systems with various closure conditions are obtained for different atmospheric models. These present the necessary conditions of well-posedness of correspondent differential boundary value problems. It is demonstrated that initialization with fixed geopotential and initialization of internal(More)
The atmosphere is a complex system supporting processes of di↵erent space and time scales. Accordingly, the complete 3D mathematical models of the atmospherecontain multi-scale solutions with fast and slow components. It is well-known that the fastest atmospheric waves are the acoustic ones, which do not contain any significant part of the atmospheric(More)