2025 , Volume 30, № 3, p.47-61

Simulation of the air flow over the sea waves requires a curved non-stationary coordinate system. When equations of motion are mapped into such coordinate systems, metric terms arise due to the changes of the shape and volume of grid cells. The paper substantiates the need to develop approximation schemes for metric terms taking into account the geometric conservation law. Both conformal coordinate system tracking the surface, the law of conservation of geometry for it, as well as a two-dimensional model of the wave boundary layer are described. A formulation for the method for approximating metric terms for this model is proposed. The implementation of the geometric conservation law by the proposed approximation scheme is justified. The numerical implementation of this model, the use of spectral representation of fields and finite difference approximation of derivatives in it is described. The results of numeric experiments based on the implemented model applied to the wave boundary layer are presented. It is shown when that using the proposed scheme, the geometric conservation law is satisfied with high accuracy. The accuracy of this law does not depend on the selected spectral (horizontal) or vertical resolution.