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Algorithms of optimal splitting in computational problems of fluid dynamics. (Russian. English summary) Zbl 1079.76599
Euler and Navier-Stokes equations of compressible gas and incompressible fluid are the base equations in numerical modeling of different aero- and hydrodynamics problems. An approximation of the equations by explicit schemes leads to large increase in computer resources, especially in three-dimensional case. Use of implicit non-factorized schemes is also non-economical due to a necessity of calculation of large-size inverse matrix. Here the author proposes difference schemes for numerical solution of three-dimensional problems of aero-hydrodynamics based on a special splitting of initial operators. The algorithms require a minimal number of arithmetic operations in their realization.

76M20 Finite difference methods applied to problems in fluid mechanics
76D05 Navier-Stokes equations for incompressible viscous fluids
76B99 Incompressible inviscid fluids
76N15 Gas dynamics (general theory)
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