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.
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Translated from Prikladnaya Matematika i Informatika, No. 51, 2016, pp. 45–51.
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Petrova, L.I. Features of Numerical Simulation of Euler and Navier–Stokes Equations. Comput Math Model 28, 32–36 (2017). https://doi.org/10.1007/s10598-016-9343-0
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DOI: https://doi.org/10.1007/s10598-016-9343-0