Splitting algorithms for numerical solution of Navier–Stokes equations in fluid dynamics problems

Implicit finite-volume predictor-corrector algorithms based on the splitting method are proposed for the numerical solution of the Navier–Stokes equations written in integral form for a compressible gas, and the properties of these algorithms are investigated. An economical algorithm for splitting equations into physical processes and spatial variables is considered. Numerical solutions of two-dimensional and spatial fluid dynamics problems are determined and compared with the known computational results. It can be concluded on the basis of the estimates obtained and calculations performed that the proposed algorithms are effective.