Author(s)

Ludmila Petrova

Department of Computational Mathematics and Cybernetics, Moscow State University, Moscow, Russia.

The analysis of integrability of the Euler and Navier-Stokes equations shows that these equations have the solutions of two types: 1) solutions that are defined on the tangent nonintegrable manifold and 2) solutions that are defined on integrable structures (that are realized discretely under the conditions related to some degrees of freedom). Since such solutions are defined on different spatial objects, they cannot be obtained by a continuous numerical simulation of derivatives. To obtain a complete solution of the Euler and Navier-Stokes equations by numerical simulation, it is necessary to use two different frames of reference.

Solutions of Two Types, Nonintegrable Manifolds and Integrable Structures, Discrete Transitions, Two Different Frames of Reference

Petrova, L. (2014) The Peculiarity of Numerical Solving the Euler and Navier-Stokes Equations. American Journal of Computational Mathematics, 4, 304-310. doi: 10.4236/ajcm.2014.44026.