The three-dimensional numerical model is based on numerical solution of the full three-dimensional system of nonlinear hydrodynamic equations for atmospheric gas in the form of conservation laws.

The numerical method is a conservative one and allows us to consider, inter alia, non-smooth solutions of nonlinear hydrodynamic equations. The method is similar to the classical Lax-Wendorff scheme.

The used method of solving of three-dimensional hydrodynamic equations is based on finite-difference approximation of the fundamental conservation laws. The system of non-linear equations of our hydrodynamic model includes: the continuity equation, the equation of motion, the equation of state for an ideal gas, the equation of energy conservation (which is transformed equivalently to the equation for pressure) and the equation for the entropy. Thus, the system of equations is overdetermined, but this redundancy is needed in case of considering of non-smooth solutions. The model takes into account viscosity and thermal conductivity, which have particularly large influence on the processes in the upper atmosphere.

The use of an implicit approximation of hydrodynamic equations at first time-half-step instead of explicit approximations is one of the important distinctions of our numerical scheme from the classical Lax-Wendorff scheme.The use of an implicit approximation of hydrodynamic equations at first time-half-step instead of explicit approximations is one of the important distinctions of our numerical scheme from the classical Lax-Wendorff scheme.

Also, the numerical scheme is characterized by using of the rickety “chess” grids with respect to spatial coordinates when different hydrodynamic variables are defined over different sub-meshes, shifted along the coordinate axes. (Our mesh is similar to the known Arakawa mesh.)Also, the numerical scheme is characterized by using of the rickety “chess” grids with respect to spatial coordinates when different hydrodynamic variables are defined over different sub-meshes, shifted along the coordinate axes. (Our mesh is similar to the known Arakawa mesh.)