DOI: https://doi.org/10.24028/gzh.0203-3100.v38i4.2016.107811

### Modified additive-averaged splitting for solving three-dimensional equations of hydrodynamics

#### Abstract

Hydrodynamic equations form the basis of modern ecological and meteorological models. The complexity of the implementation of such models is due to three-dimensionality and nonlinearity of the equations, as well as large amounts of data and the need for prompt solutions. The use of parallel computing for solving hydrodynamic systems entered in the world practice. This approach makes it possible to reduce solution time significantly, but requires the development of new methods of implementation of the model equations. The described method for solving three-dimensional equations of convective diffusion is a modification of additive-averaged splitting three-dimensional equations. The modification carried out to increase the efficiency of splitting for the parallel computing. The essence of the modification is the introducing a parameter that indicates the number of steps, on which one-dimensional problems are solved by an explicit account in parallel on different processors without exchange of data between them. The results of numerical experiments that confirm the good accuracy, convergence and efficiency of the proposed method are shown.

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