Features of Numerical Simulation of Euler and Navier–Stokes Equations

Abstract

The Euler and Navier–Stokes equations are shown to have double solutions: one on a nonintegrable tangent bundle and one on integral structures. The transition from solutions of first to second type describes a transition of the gas-dynamic system from an equilibrium to a local equilibrium, with the formation of vorticity and turbulence. Such processes can be described only in two coordinate systems or by simultaneously solving the equations both numerically and analytically.