Construction of parallel algorithms for modeling hydrodynamic processes in the Azov Sea based on hybrid MPI+OpenMP technology

A mathematical model is proposed to calculate three-dimensional fields of the velocity vector of the aquatic variable-density environment using the equations of motion (Navier-Stokes) and the continuity equation, regularized according to B.N. Chetverushkin. When solving the three-dimensional problems of diffusion-convection for areas that are significantly less in extent along one of the directions than in the other two spatial directions (shallow water bodies), the schemes of sequential splitting of the problems into a two-dimensional problem along the horizontal and a one-dimensional problem along the vertical are used. The calculation of the two-dimensional problem is carried out according to an explicit scheme, while the one-dimensional problem is calculated on the basis of a weights scheme. The use of this scheme makes it possible to eliminate the main drawback of the explicit scheme - a strict constraint on the time step. The specified accuracy is achieved at time steps that are 10-30 times greater than those of the explicit scheme. Parallel algorithms are constructed to solve the hydrodynamic grid problems arising from their numerical implementation in three-dimensional regions with a “prolate geometry” by the alternating-triangular method and by splitting into two-dimensional and one-dimensional problems. The parallel algorithms based on hybrid technology demonstrate their advantage over the standard algorithms developed using MPI technology and oriented to supercomputing systems. The results obtained when launching the created software show the high efficiency of the algorithms developed to study the hydrophysical processes in the Sea of Azov using the methods and tools of mathematical modeling.