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Springer Proceedings in Earth and Environmental Sciences

ISSN:2524342

2023

Sklyar, S.N.¹

10.1007/978-3-031-25962-3_16

The aim of the work is to compare the exact analytical solution for a three-dimensional wind flow model with its numerical analogue for testing and analyzing difference discretizations and computational algorithms used in integrating the dynamic model. When integrating the equation for the current function, a multi-parametric family of difference schemes is considered, which, under certain parameters, includes schemes of central difference, directional difference, schemes of A. A. Samarsky and A. M. Ilyin. To find the velocity fields by the found current function, a projection version of the integro-interpolation method (PVIIM) is used. The results of calculations of the current function and integral velocities are compared with an analytical solution. As a result of numerical experiments, it is shown that the best results are obtained when using the Ilyin scheme and when using approximations of derivatives based on the PVIIM method. The implemented testing of difference schemes and algorithms, comparison of the results of calculations with an accurate analytical solution made it possible to implement a reasonable choice of discretizations for integrating the equations of the wind circulation model. The constructed difference discretizations allow, under all other equal conditions, to increase the accuracy of reproduction of the desired numerical solution of the model. © 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.

Analytical solution, Current function, Difference schemes, Dimensionless problem, Wind currents

2023-05-05 14:14:24