Modified additive-averaged splitting for solving three-dimensional equations of hydrodynamics
© L.N. Katsalova, 2016
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.
Key words: hydrodynamics, convection diffusion equation, parallel computing, additive-averaged splitting, explicit account method.