Predictor-corrector method for numerical solution of Euler and Navier–Stokes equations

A generalization of the schemes of optimal splitting for the numerical solution of the Euler and Navier–Stokes equations in the curvilinear transformed coordinates is performed in this paper. We introduce splitting of the equations, which is uniform in their divergent and non-divergent forms and allows us to construct a class of economic difference schemes. They are realized by scalar sweep methods on the fractional steps and have a large stability margin. The offered algorithm has been tested on stationary and non-stationary problems.